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Resource Allocation and Decision Analysis (ECON 8010) – Spring 2014 “Overview of Alternative Competitive Environments” Definitions and Concepts: Profit – Total Revenues minus Total Costs. Primary objective of most private enterprise is to maximize profit
“Cost-Benefit Principle” – a rational decision maker should undertake an action if and only
if the Marginal Benefit from taking the action is at least as great as the Marginal Cost of doing so.
For profit maximization, think about increasing quantity produced/sold and comparing
Marginal Revenue to Marginal Costs
In general, if a firm sells (Q) units of output each at a price of (P), then Total Revenue is equal to (Q)(P) => but, the behavior of Marginal Revenue depends greatly upon the Market Structure in which the firm operates
Continuum of Market Structure: Market Power – a firm has market power if: (i) it can increase the price of its product
without losing all customers, or equivalently (ii) it must decrease the price of its product in order to sell additional units.
“Market Power” “control over price” Firms in “perfectly competitive markets” have “no market power” [face a “horizontal
demand curve” at the market price determined by the interplay of market demand and market supply]
Firms in “imperfectly competitive markets” (i.e., all other market structures) have at least “some market power” [“downward sloping demand curve”]
Monopoly Perfect
Competition Intermediate Market Structures (e.g., Duopoly,
Oligopoly, Monopolistic Competition)
Marginal Revenue – the change in Total Revenue as quantity sold is increased If demand is given by the Inverse Demand Function )(qPD
, then qqPqR D )()( , and it follows that )()()( qPqqPqMR DD
Price Elasticity in terms of Inverse Demand: qqP
qP
Q
P
P
Q
D
D
QP
PP
p )(
)(1
%
%
From here, )(
)(1
qP
qqP
D
D
p
=> Marginal Revenue can be expressed as
pD qPqMR
1
1)()(
Fixed Costs – costs that do not vary in magnitude as the quantity of output produced is
changed Variable Costs – costs that do vary in magnitude as the quantity of output produced is
changed Total Costs are equal to the sum of Variable Costs and Fixed Costs: FqVCqC )()( . Average Total Costs – Total Costs divided by quantity of output produced =>
q
qCqATC
)()(
Average Variable Costs – Variable Costs divided by quantity of output produced =>
q
qVCqAVC
)()(
Average Fixed Costs – Fixed Costs divided by quantity of output produced =>
q
FqAFC )(
Average Total Costs are equal to the sum of Average Variable Costs and Average Fixed
Costs: )()(
)()()()( qAFCqAVC
q
F
q
qVC
q
FqVC
q
qCqATC
Marginal Costs – the change in Total Costs as quantity of output produced is increased =>
)()()( qCVqCqMC Efficient Scale – the efficient scale of production refers to the quantity of output at which
Average Total Costs of production are minimized.
Short Run – a period of time sufficiently short so that the amount hired/used of at least one input is equal to some predetermined level (based upon a previous decision) In the short run, the “fixed inputs are being hired in predetermined quantities” => “fixed
costs represent the predetermined costs of hiring these fixed inputs in their predetermined quantities”
Long Run – a period of time sufficiently long so that the amount hired/used of every input can be varied In the Long run the firm has the flexibility to hire “zero units of every input” => “incur
zero costs of production” => “fixed costs are equal to zero” => “all costs are variable” Optimal Choice of Output in Short Run by a firm in a Perfectly Competitive Market: a
firm in a perfectly competitive market (in which the prevailing price for output is p ) maximizes profit by:
(i) ‘shutting down’ and producing 0q units of output if minAVCp (ii) producing the positive quantity of output q for which pqMC )( (with MC
intersecting MR ‘from below’) if minAVCp Long Run Dynamics of Perfectly Competitive Market => recall, a Perfectly Competitive
Market is characterized by “Free Entry/Exit” in the Long Run If firms “currently in the market” are earning positive profits in the Short Run, then:
o New firms will enter the market, increasing market supply o Increase in supply leads to a decrease in equilibrium price, driving down profits of
firms in the industry o Entry will continue and price will gradually decrease until profit of firms in the
industry is driven down to zero If instead firms “currently in the market” are earning negative profits in the Short Run,
then: o Some existing firms will exit the market, decreasing market supply o Decrease in supply leads to an increase in equilibrium price, driving up profits of
firms in the industry o Exit will continue and price will be gradually increase until profit of firms in the
industry is driven up to zero In either case, the outcome of this process is one in which firms in the industry are
earning “zero profit” Since )()()( qATCpqqCpqq this condition of “zero profit” implies
)(qATCp at the Long Run equilibrium o If price is driven to )(qATCp in the Long Run and firms are still maximizing profit
in the Short Run (i.e., )(qMCp ), it follows that in the Long Run we must have )()( qATCqMCp => firms are operating at the point where )(qATC is
minimized (i.e., at the “Efficient Scale” of production), thereby minimizing the industry’s total costs of production
Explicit Costs – inputs costs that require an outlay of money by the firm (i.e., costs
associated with paying an “out-of-pocket expense” to acquire/use a factor of production). Implicit Costs – inputs costs that do not require an outlay of money by the firm (i.e., costs
associated with incurring a “non-monetary, opportunity cost” to acquire/use a factor of production).
Total Economic Costs – a notion of costs which includes “all costs” of hiring inputs, both explicit costs and implicit costs (i.e., Total Economic Costs are equal to the sum of Explicit Costs and Implicit Costs). Assume that (unless otherwise noted), “Total Costs” refer to “Total Economic Costs”
(i.e., “Total Costs” include not only Explicit but also Implicit Costs) Accounting Profit – a measure of profit defined as the difference between Total Revenues
and Total Explicit Costs Economic Profit – a measure of profit defined as the difference between Total Revenues and
Total Economic Costs Assume that (unless otherwise noted), “Profit” refers to “Economic Profit”
Relation between Accounting Profit and Economic Profit. (Accounting Profit) = (Total Revenues) – (Total Explicit Costs) (Economic Profit) = (Total Revenues) – (Total Economic Costs)
= (Total Revenues) – (Total Explicit Costs + Total Implicit Costs) = (Total Revenues) – (Total Explicit Costs) – (Total Implicit Costs) = (Accounting Profit) – (Total Implicit Costs)
(Accounting Profit) = (Economic Profit) + (Total Implicit Costs) Inverse Elasticity Pricing Rule – to maximize profit, a firm must be operating where the
“markup of price above marginal costs as a percentage of price” is equal to “minus the inverse of price elasticity of demand.”
When demand is “less elastic” (i.e., p closer to zero consumers not very sensitive to
price), a firm with market power will set a price for which the “percentage markup of price over MC” is greater
Total Social Surplus – a measure of the total gains to society from economic activity in a
market As long as there are no “external effects,” Total Social Surplus is equal to the sum of
Total Consumers’ Surplus and Total Producers’ Surplus Deadweight Loss (DWL) – the difference between the “maximum possible level of Total
Social Surplus” and the “realized level of Total Social Surplus.” DWL is zero at the efficient level of trade DWL is positive at all other levels of trade.
Inefficiency from “too little trade” – there are some units that are not traded for which
trade would generate a positive net gain for society i.e., we don’t trade all units that we should trade (absent external effects) these are units that are not traded even though buyer’s
reservation price is greater than seller’s reservation price
Inefficiency from “too much trade” – there are some units that are traded for which trade generates a negative net gain for society i.e., we trade some units that we should not trade (absent external effects) these are units that are traded even though seller’s reservation
price is greater than buyer’s reservation price Monopoly – a market structure in which there is one single seller of a unique good (for
which there are no close substitutes) and in which there are significant barriers to entry which prevent rival firms from entering the market in many respects, “Monopoly” is the polar opposite of “Perfect Competition” in the Long Run (since entry barriers prevent new firms from entering the market) a
monopolist can potentially earn a positive profit period after period Monopolistic Competition – market structure in which competing firms sell differentiated
products (and thus, each firm has some market power in the Short Run) and in which there are no substantial barriers to entry examples: gas stations, pharmacies, restaurants, and grocery stores; novels; movies in the Long Run “free entry” will result in “many firms” bring in the market (with profit
of each firm being driven to zero) [we’ll expand upon this below] Oligopoly – market structure in which firms sell very similar products (i.e., “slight
differentiation”), but in which there are significant barriers to entry which prevent most potential rivals for entering the market Examples: “Coke/Pepsi,” “XBox/Playstation/Wii” In most respects, closer to “Pure Monopoly” than to “Perfect Competition” Because of entry barriers, there will end up being “relatively few firms” in the market in
the Long Run There is no “one-size-fits-all” model of Oligopoly => will develop and analyze multiple
models later in the course Four Firm Concentration Ratio (C4) – a measure of industry concentration defined as the
percentage of total industry sales made by the four largest firms in the industry (C4 ranges between 0 and 100 – a higher value suggests the industry is more concentrated or less competitive).
Herfindahl-Hirschman Index (HHI) – a measure of industry concentration defined as the
sum of the ‘squared values of market shares’ over all firms in the industry (HHI ranges
between 0 and 2100 10,000 – a higher value suggests the industry is more concentrated or less competitive).
Selected “Real World” Values of C4 and HHI: Industry: C4: HHI:
Electric Light Bulbs 88.9 2849.0 Breakfast Cereals 82.9 2445.9
Automobiles 79.5 2862.8 Aluminum Sheet/Plate/Foil 65.0 1447.0 Telephone Equipment 55.3 1061.1 Women’s Footwear 49.5 794.8
Soft Drink Manufacturing 47.2 800.4 Semiconductors 41.7 688.7
Computers and Peripherals 37.0 464.9 Cement Manufacturing 33.5 466.6
Petroleum Refineries 28.5 422.1 Paper Manufacturing 18.5 173.3 Textile Mills 13.8 94.4
Relation between Marginal Revenue and Price for… (i) Firm with “no market power”
faces horizontal demand curve => “perfectly elastic demand” or p
pqPqPqMR DD )(01)()( => Marginal Revenue is constant and equal to price
Intuitive: when price is simply equal to some constant p regardless of quantity sold, then selling one more unit always increases revenue by exactly p dollars
(ii) Firm with some “market power” or “control over price”
Faces downward sloping demand => 0 p
pD qPqMR
1
1)()( => Thus, for a firm with “market power” Marginal Revenue is:
“Less than Price.” Visually:
Positive 1p (dropping price and increasing quantity demanded leads to
greater revenue) Negative 01 p (dropping price and increasing quantity demanded leads to
less revenue) Equal to zero (which must be true if total revenue is maximized) 1p
q 0
$
0
pqPD )( =>
pqMR )(p
q 0
$
0 )(qMR
)(qPD
Graphical illustration of Costs of Production: Efficient Scale – the efficient scale of production refers to the quantity of output at which Average Total Costs of production are minimized. For the “first unit of output,” Variable Costs are equal to simply “marginal costs of the first
unit” => AVC(q) must start out equal to MC(q)… But “total costs for the first unit” consist of more than just “variable costs of the first unit” =>
ATC(q) will start out above MC(q)… Since ATC = AVC + AFC => AFC = ATC – AVC AFC is the “vertical distance between ATC and AVC” Since AFC decreases as (q) increases => red curve and blue curve must get closer to each
other as (q) increases
$
0
0
q
MC(q)
ATC(q) Minimum level of Average Total Costs
AVC(q)
Minimum level of Average
Variable Costs
Quantity of output which minimizes
AVC(q)
“Efficient Scale” – Quantity of output
which minimizes ATC(q)
Short Run choice of output and profitability of a firm in a Perfectly Competitive Market: Thus, the “short run supply curve” of this firm is essentially: the portion of the Marginal Cost Curve which lies above the Average Variable Cost Curve.
For “all possible positive prices” we have that a profit maximizing firm operating in a perfectly competitive market in the short run will:
$
0
0
quantity
MC(q)
AVC(q)
quantity at which AVC are minimized
Minimum value of AVC
Short Run Supply Curve of Firm=> curve illustrating ‘quantity supplied as a function of price’ (at all possible market prices)
Minimum Value of Average Variable Costs
‘Shut Down’ and produce zero units of output
Earn a profit of (–F)
Price of Output
0
Minimum Value of Average Total Costs
Produce a positive quantity of output
Able to earn a positive profit
Produce a positive quantity of output
Maximum profit is negative, but greater than (–F)
Short Run Profit Maximization for firm with Market Power: maximize profit by charging P* per unit and selling Q* units of output (Profit) = (Total Revenues) – (Total Costs) = [P*][Q*] – [Q*][ATC(Q*)] = [Q*][P* – ATC(Q*)] = (“light green area above”) In the graph above (Profit)>0 => but, even a firm with market power is not guaranteed a
positive profit (if the height of the ATC(q) curve was greater than the height of the Demand curve at every quantity, then maximum profit would be negative)
In fact, it may be best for a firm with market power to “shutdown” and produce zero units of output in the Short Run => if the height of the AVC(q) curve was greater than the height of the Demand curve at every quantity, then the firm would maximize profit by producing zero units of output in the Short Run (and realizing a profit of (– F))
When a firm with market power maximizes profit, a positive Deadweight-Loss results:
$
0
0
quantity
MC(q)
ATC(q)
MR(q)
Demand
Q*
P*
ATC(Q*)
$
0
0
quantity
MC(q)
MR(q)
Demand
Q* QE
DWL
P*
CS PS
Numerical Examples of Industry Concentration Measures: Suppose we observe the following “market shares” (i.e., fractions of “total industry output”
or of “total industry revenues” across several different industries)…
Industry A Industry B Industry C Industry D Industry E 20 30 65 70 20 20 15 5 3 20 20 10 5 3 20 20 8 5 2 20 4 6 4 2 20 4 5 4 2 3 5 3 2 3 5 3 2 2 4 2 2 2 4 2 2 1 3 1 2 1 3 1 2 2 2 2 2
A: (C4) = (20+20+20+20) = 80 (HHI) = ( 222222222222 1122334420202020 ) = 1,660 B: (C4) = (30+15+10+8) = 63 (HHI) = ( 2222222222222 2334455568101530 ) = 1,454 C: (C4) = (65+5+5+5) = 80 (HHI) = ( 222222222222 1122334455565 ) = 4,370 D: (C4) = (70+3+3+2) = 78 (HHI)=( 222222222222222 2222222222223370 )=4,966 E: (C4) = (20+20+20+20) = 80 (HHI) = ( 22222 2020202020 ) = 2,000 Observations from the preceding numerical example… Value of (C4) does not depend upon “anything beyond the 4th firm” => compare “Industry A” to
“Industry E” Value of (C4) does not depend upon “how the market shares are distributed among the ‘Top 4’ firms”
=> compare “Industry A” to “Industry C” Across two different industries: there can be “big differences in structure” with only “small
differences in the value of (C4)”; and further the “ordinal values of (C4)” might “run counter to our intuition” => compare “Industry D” to “Industry A or E” (clearly “D” is “closer to Monopoly,” but it has a smaller value of (C4)…)
(HHI) and (C4) can give “different orderings” C4: A, C, and E are “tied” for “closest to Monopoly,” and are “closer to Monopoly” than D HHI: ordering from “closest to Monopoly” to “closest to Perfect Competition” of: D, C, E, A, B
“Monopolistically Competitive” Market in Long Run: (i) Suppose Short Run Profits are Positive (i.e., ATC(q) “dips below” demand) => “new
firms” want to enter (and can since there are “no barriers to entry”) Entry of “new firms” increases the “available options for consumers” => thereby
“reducing demand” for all individual firms initially in the market Continued entry occurs until demand for each firm decreases enough so that profit of the
firm is driven down to zero (ii) Suppose Short Run Profits are Negative (i.e., ATC(q) is “above” demand everywhere) =>
“existing firms” want to exit Exit of “existing firms” decreases the “available options for consumers” => thereby
“increasing demand” for all firms which remain in the market Continued exit will occur until demand increases enough so that profit of each firm is
driven up to zero Short Run situation after entry or exit has occurred to the point where profit of the firm is driven to zero => whether we “start with positive profits” or “start with negative profits,” the market will reach the “same state” in the Long Run…
Demand “just barely touches” (and is everywhere else “below”) the Average Total Cost
Curve => “zero profit” This point of “tangency” between Demand and ATC occurs at the one unique quantity at
which Marginal Revenue is equal to Marginal Costs Two notable features of the Long Run Equilibrium in Monopolistically Competitive Market:
1. due to the “competitive nature” of the market (i.e., entry is possible), Long Run profits are driven to zero => price is equal to Average Total Costs
2. because firms have market power, demand is downward sloping and marginal revenue is therefore less than price => firms produce a quantity of output for which price is greater than Marginal Costs (positive DWL from “too little trade”)
$
0
0
quantity
MC(q)
ATC(q)
MR(q)
Demand
Q*
ATC(Q*)=P*
Comparison of Monopolistic and Perfect Competition in LR:
Monopolistically Competitive Market: in the Long Run, sell *Q , each at a price of
*)(*)(* QMCQATCP
Perfectly Competitive Market: in the Long Run, sell PCQ , each at a price of
)()( PCPCPC QATCQMCP
Excess Capacity – amount by which the output of a firm is less than the “efficient scale” of output a firm with “excess capacity” could decrease ATC of production by increasing output =>
in a monopolistically competitive market, the industry’s total costs of production are not minimized
Markup: Monopolistically Competitive firm charges a price above “marginal costs of the last unit produced” (a Perfectly Competitive firm charges “(price)=(MC)”) “Would you want another customer come through the door ready to buy at your current
price?” – “yes” for Monopolistically Competitive firm but “don’t care” for Perfectly Competitive firm
$
0
0
quantity
MC(q)
ATC(q) MR(q)
Demand
PCQ*Q
**)( PQATC
PCPC PQMC )( )( PCQATC
“Excess Capacity”
Multiple Choice Questions: 1. __________________ is a market structure in which firms sell differentiated products
(and thus, each firm has some “market power” in the Short Run) and in which there are no substantial barriers to entry in the Long Run.
A. Monopolistic Competition B. Oligopoly C. Monopoly D. Perfect Competition 2. Suppose that as the price of shoes decreases from $40 to $35 Total Consumer
Expenditures on shoes increases from $800,000 to $840,000. From this information we can infer that over this price range demand is
A. Inelastic. B. Unit Elastic C. Elastic.
D. None of the above answers are necessarily correct (based upon the given information).
3. Consider a market in which the efficient level of trade is 28,000 units. If 31,500 are
traded, then Deadweight Loss A. would be positive. B. would be equal to zero. C. would be negative. D. could possibly be positive or negative (it depends upon “how elastic” demand is). 4. In “Industry X”: the largest firm produces 25% of total industry output, the second largest
firm produces 15% of total industry output, and the third largest firm produces 9% of total industry output. From this information alone we know that
A. this market is “Perfectly Competitive.” B. the value of the “Four Firm Concentration Ratio” is greater than 49.
C. the value of the “Herfindahl-Hirschman Index” in this industry is exactly equal to 931.
D. More than one (perhaps all) of the above answers is correct. 5. The “Efficient Scale of Production” refers to A. the level of output above which all Fixed Costs can be avoided. B. the level of output which minimizes Average Fixed Costs of production. C. the level of output which minimizes Average Total Costs of Production.
D. the level of output at which Marginal Costs of Production become negative. 6. In which of the following industry structures is there “free entry”? A. Monopolistic Competition. B. Oligopoly. C. Perfect Competition.
D. More than one (perhaps all) of the above answers is correct.
7. __________________ provides a direct, general measure of the “total gains to society from economic activity in a market.”
A. Deadweight-Loss B. Monopoly Surplus C. Total Social Surplus D. Profit 8. For a firm with “market power” ________________, while for a firm in a “perfectly
competitive market” ________________. A. Marginal Revenue is equal to Price; Marginal Revenue is less than Price. B. Marginal Revenue is less than Price; Marginal Revenue is greater than Price.
C. Marginal Revenue is less than Price; Marginal Revenue is equal to Price. D. Marginal Revenue is greater than Price; Marginal Revenue is equal to Price. 9. The _______________ is defined as a period of time sufficiently long so that the amount
hired/used of every factor of production can be altered. A. Profitability Stage B. Efficient Scale of Production C. Short Run D. Long Run 10. “Excess Capacity” refers to
A. the difference between Revenue and Variable Costs of Production. B. the maximum possible amount of output that a firm can produce.
C. the amount by which the output of a firm is less than the “efficient scale” of output.
D. the amount by which the output of a firm has increased between the last period of production and the current period of production.
11. According to the “Inverse Elasticity Pricing Rule,” when maximizing profit a firm must
be operating in a manner so that
p1 is equal to
A. P . B. MCP .
C.
MC
P .
D.
P
MCP .
12. The ____________________ states that a rational decision maker should undertake an
action if and only if the Marginal Benefit from taking the action is at least as great as the Marginal Cost of doing so.
A. Cost-Benefit Principle B. Incentive Principle C. Inverse Elasticity Pricing Rule D. Herfindahl-Hirschman Index
13. In which of the following industry structures should a firm expect to earn “zero profit” in the Long Run?
A. Perfect Competition. B. Monopolistic Competition. C. Monopoly. D. More than one (perhaps all) of the above answers is correct. For questions 14 through 17, consider a firm with costs of production as illustrated below: 14. Based upon the graph above, this firm is currently operating in the A. Long Run, since no Marginal Cost Curve has been drawn.
B. Long Run, since Average Fixed Costs clearly increase as more output is produced.
C. Short Run, since Marginal Costs of production are clearly positive. D. Short Run, since Fixed Costs of Production are clearly positive. 15. The Marginal Cost of producing the 900th unit of output must be A. exactly equal to $5.60. B. greater than $5.60, but less than $7.25. C. exactly equal to $7.25. D. greater than $7.25. 16. The “Efficient Scale” of production is equal to __________ units of output.
A. 0 B. 200 C. 800 D. 1,000
17. If this firm were to produce 1,000 units of output, Average Variable Costs of Production
would be equal to A. 50¢. B. $5.60. C. $5.75. D. $8.75.
$
0
0
quantity
ATC(q)
AVC(q)
95.6 25.7min ATC
60.5min AVC
45.14
00.8
200 800 000,1
18. Consider the “automobile” industry and the “textile mills” industry. The value of the “Herfindahl-Hirschman Index” for “automobiles” is (2,862.8), while the value of the “Herfindahl-Hirschman Index” for “textile mills” is (94.4). These values directly suggest that A. both the “textile mills” and “automobile” industries are “Pure Monopolies.” B. producers of automobiles incur production costs which are over 30 times greater
than the production costs incurred by textile mills. C. the total value of output produced by automobile factories is over 30 times greater
than the value of output produced by textile mills. D. the “automobile” industry is less competitive than the “textile mills” industry.
For questions 19 through 21, consider a monopolist operating in the market illustrated below. Suppose throughout that the monopolist is restricted to charging a common price for every unit of output sold. 19. In order to maximize profit this monopolist should A. sell 1,000 units of output. B. sell 400 units of output C. charge a price of $2 per unit. D. More than one (perhaps all) of the above answers is correct. 20. The “efficient level of trade” in this market is A. 400 units. B. 600 units. C. 1,000 units. D. 1,200 units. 21. The maximum profit of this monopolist would be exactly equal to $0 if Fixed Costs were A. exactly equal to $600 B. exactly equal to $1,000 C. exactly equal to $1,400
D. None of the above answers are correct (since a monopolist is always able to earn a positive profit).
$
0
0
quantity
MC(q)
MR(q)
Demand
AVC(q)
400
3.00
3.50
2.00
5
1,000 1,200
1.00
600
22. Scott sells turnips in a small, rural town in Oklahoma. Since he is the only turnip seller in town, he has some “market power.” He is currently charging $1.75 for each five pound bag of turnips, a price at which he sells 400 bags per month. If he were to increase his quantity sold to 500 bags per month
A. he would have to decrease the price he charges. B. his Average Total Costs of production would have to be lower. C. his Total Revenue would have to increase. D. More than one (perhaps all) of the above answers is correct. For questions 23 through 25, consider a firm in a perfectly competitive market with costs of production as illustrated below:
23. If this firm were to produce zero units of output in the short run, then A. it would earn zero profit. B. it would earn a profit of $(– 2,520). C. it would earn a profit of $(– 6,000). D. it would earn a profit of $(– 6,090). 24. If the per unit price of output in this market were $12.00, then this firm would A. produce 2,400 units of output. B. incur Variable Costs of Production equal to $15,600. C. earn a profit of $13,200. D. More than one (perhaps all) of the above answers is correct. 25. This firm will produce a positive quantity of output in the short run but earn a negative
profit if and only if the per unit price of output is A. less than $3.15. B. less than $4.35. C. exactly equal to $4.35. D. greater than $4.35 but less than $8.50.
$
0
0
quantity
MC(q)
ATC(q)
AVC(q) 50.8min ATC
35.4min AVC
15.3min MC
50.5
2,000 1,400 800 2,400
00.9
00.12
50.6
26. “Average Total Costs of Production” A. are equal to “Average Variable Costs of Production” plus “Average Fixed Costs
of Production.” B. are defined as Fixed Costs of Production divided by quantity of output produced.
C. can never be less than “Average Variable Costs of Production.” D. More than one (perhaps all) of the above answers are correct. 27. The “short run supply curve” of a firm in a perfectly competitive market is A. a horizontal line at the prevailing market price.
B. a horizontal line at the minimum value of Average Total Costs of Production. C. the portion of the Marginal Cost curve which lies above the Average Variable
Cost Curve. D. the portion of the Marginal Cost curve which lies above the Average Total Cost
Curve. 28. Consider a firm with costs of production given by 000,153)( qqC , facing demand of
)2/3(
500,94)(
ppD (i.e., quantity demanded as a function of price is equal to “94,500
divided by price raised to the power of three-halves). When maximizing profit this firm A. is not able to earn a positive profit. B. should charge a price of $3 per unit. C. should sell 3,500 units of output. D. More than one (perhaps all) of the above answers is correct.
29. Consider a firm in a perfectly competitive market with: output price of $4.95 per unit; minAVC $5.20; and minATC $6.85. When maximizing profit in the short run, this
firm A. will shut-down and earn a negative profit. B. will shut-down and earn zero profit. C. will produce a positive quantity and earn a negative profit. D. will produce a positive quantity and earn a positive profit. 30. ______________ refer(s) to input costs that do not require an outlay of money by the
firm. A. Profit
B. Implicit Costs C. Explicit Costs D. Accounting Costs 31. If a firm made an Accounting Profit of $750,000 last year, then the Economic Profit of
the firm A. must have been greater than $750,000. B. must have also been equal to $750,000. C. must have been less than $750,000 (but had to have been positive).
D. must have been less than $750,000 (and could have been either positive or negative).
Problem Solving or Short Answer Questions: 1. Consider a market in which demand is given by the demand function
ppD 000,2000,16)( . 1A. Is demand Elastic, Inelastic, or Unit Elastic at a price of 2p ? Explain.
1B. If price were to decrease from 23.6p to 89.5p would Total Consumer Expenditures on this good increase, decrease, or remain constant? Explain.
1C. Is it possible for Total Consumer Expenditures on this good to equal $35,000? Clearly explain why or why not.
2. Consider a firm operating in a perfectly competitive market with production costs of
000,520)( 2800
1 qqqC .
2A. Determine expressions for )(qMC , )(qAVC , and )(qATC for this firm. 2B. Determine an exact price above which the firm will choose to sell a positive
quantity of output in the Short Run and below which the firm will choose to shut-down in the Short Run.
2C. Determine a function which specifies the quantity of output that this firm will choose to produce in the Short Run (as a function of market price, p ).
2D. For what range of values of p is this firm able to earn a positive profit in the Short Run? For what range of values of p is this firm not able to earn a positive profit in the Short Run? Explain.
3. Consider a firm operating in a perfectly competitive market with production costs of
500,15)( 2513
2251 qqqqC .
3A. Determine the functional form of )(qMC . 3B. Determine the functional form of )(qAVC . 3C. Determine the functional form of )(qATC .
3D. Determine an exact price above which the firm will choose to sell a positive quantity of output in the Short Run and below which the firm will choose to shut-down in the Short Run.
4. Consider a firm with production costs of FqqC 5
16)( , facing demand of
25.1
800,648)(
ppD .
4A. Determine the per unit price that this firm would set and the quantity of output that this firm would sell in order to maximize profit.
4B. For what range of values of F is this firm able to earn a positive profit in the Short Run? For what range of values of F is this firm not able to earn a positive profit in the Short Run? Explain.
5. Consider a firm operating in a perfectly competitive market in the Short Run. The table below provides a partial summary of costs of production for this firm. (Assume throughout that the firm is restricted to choosing from only the quantities of output corresponding to each of the rows in the table below; in this context, Marginal Costs are equal to the change in Total Costs divided by the change in Quantity of Output produced – that is, Q
TCMC ).
Quantity of Output
Variable Costs
Fixed Costs
Total Costs
Marginal Costs
Average Variable Costs
Average Fixed Costs
Average Total Costs
0 0
20,000 2,000
20 179,200
60,000 6,640
40 2,000
50 4,824
58 127,600 2,400
5,400 2,500 4,675
5A. Complete the table above by correctly filling in all of the missing numerical values.
5B. If this firm is able to sell its output for $3,000 per unit, how much output would it sell, how much revenue would it earn, and is it able to earn a positive profit?
5C. If this firm is able to sell its output for $5,000 per unit, how much output would it sell, how much revenue would it earn, and is it able to earn a positive profit?
6. Dan is the President and CEO of “Owl Softdrinks,” the producer of “Scrappy Cola.” The
consumer research division of “Owl Softdrinks” recently told Dan that under current market conditions (i.e., for the demand that the firm currently faces and at the price that the firm is currently charging) the Price Elasticity of Demand for “Scrappy Cola” is approximately (–0.79). Assuming that this value has been estimated correctly, what can you infer about the current pricing and output decision of this firm?
7. Consider a firm with production costs of 7504)( 2
1001 qqqC , facing demand given
by the inverse function qqPD 200113)( .
7A. Determine expressions for )(qMC and )(qMR for this firm. 7B. Determine the per unit price that this firm would set and the quantity of output
that this firm would sell in order to maximize profit. 7C. Determine the quantity of output that would maximize Total Social Surplus in this
market. 7D. Determine numerical values for Total Consumers’ Surplus, Total Producer’s
Surplus, Profit, and Deadweight-Loss in this market. 7E. Determine an expression for “Price Elasticity of Demand as a function of quantity
sold” for the inverse demand function given above. 7F. Verify that when maximizing profit, the firm is choosing a price and quantity for
which the Inverse Elasticity Pricing Rule is satisfied.
Answers to Multiple Choice Questions:
1. A 2. C 3. A 4. B 5. C 6. D 7. C 8. C 9. D 10. C 11. D 12. A 13. D 14. D 15. B 16. D 17. C 18. D 19. B 20. B 21. B 22. A 23. C 24. D 25. D 26. D 27. C 28. C 29. A 30. B 31. D
Answers to Problem Solving or Short Answer Questions: 1A. Inelastic. Note that the given demand function of ppD 000,2000,16)( describes a
linear demand relationship. The corresponding linear demand curve has a vertical intercept of 8p and a horizontal intercept of 000,16q . Thus, the point along the demand curve at a price of 2p lies on the “bottom half of the demand curve.” Recall that for any linear demand curve, demand is Inelastic along the “bottom half of the curve.”
1B. Increase. A decrease in price from 23.6p to 89.5p is a movement down this linear demand curve along the “top half of the demand curve.” Recall that for any linear demand curve, demand is Elastic along the “top half of the curve.” Further, when
demand is Elastic, a decrease in price will (in general) lead to an increase in Total Consumer Expenditures on the good. Thus, this decrease in price leads to an increase in Total Consumer Expenditures.
1C. No, given this demand function it is not possible for Total Consumer Expenditures to equal $35,000. Recall that in general Total Consumer Expenditures can be increased: if demand is Elastic by decreasing price, and if demand is inelastic by increasing price. It follows that along any linear demand curve, Total Consumer Expenditures are maximized at the one point where demand is unit elastic (the “halfway point of the curve”). For the demand function ppD 000,2000,16)( this halfway point corresponds to a price of
4p and quantity of 000,8q . Thus, Total Consumer Expenditures are maximized when 8,000 units are purchased each at a price of $4. This leads to Total Consumer Expenditures of 000,35$000,32$)000,8)(4($))(( qp .
2A. Given the cost function 000,520)( 2
8001 qqqC : 20)()( 400
1 qqCqMC ,
20)(
)( 8001 q
q
qVCqAVC , and
q
qCqATC
000,520
)()( 800
1 .
2B. The firm will choose to sell a positive quantity of output in the Short Run if and only if price is greater than the minimum value of Average Variable Costs of production. From
the function 20)(
)( 8001 q
q
qVCqAVC , it is straightforward to see that the minimum
value of Average Variable Costs over all possible 0q is realized at 0q :
20)0(min AVCAVC . 2C. So long as price is greater than or equal to $20, the firm maximizes profit by producing
the positive quantity for which )(qMCp . Given 20)( 4001 qqMC , this condition is
204001 qp . Solving for q as a function of p , we obtain 000,8400)( ppS .
2D. A firm in a perfectly competitive market will be able to earn a positive profit in the Short Run so long as price is greater than the minimum value of Average Total Costs of production. Recall that at the point where )(qATC achieves its minimum value, we must have )()( qATCqMC . Thus, we can determine the quantity of output that minimizes )(qATC by setting )()( qATCqMC and solving for q . Doing this:
)(20000,5
20)( 4001
8001 qMCq
qqqATC 000,000,42 q 000,2q .
From here it follows that 25)000,2(min ATCATC . Therefore, the firm is able to earn a positive profit in the Short Run if and only if per unit price is above $25.
3A. For 500,15)( 2
513
2251 qqqqC we have 5)()( 5
222253 qqqCqMC .
3B. For 500,15)( 2513
2251 qqqqC we have 5
)()( 5
122251 qq
q
qVCqAVC .
3C. For 500,15)( 2513
2251 qqqqC we have qqq
q
qCqATC 500,1
512
2251 5
)()( .
3D. In the Short Run the firm maximizes profit by shutting-down and selling zero units of output if and only if price is below the minimum value of Average Variable Costs of Production. Recall that at the point where )(qAVC achieves its minimum value, we must have )()( qAVCqMC . Thus, we can determine the quantity of output that minimizes )(qAVC by setting )()( qAVCqMC and solving for q . Doing this:
)(55)( 522
2253
512
2251 qMCqqqqqAVC qq 5
122252 5.2210
225 q .
From here it follows that 75.2510225
512
10225
2251
10225
min AVCAVC . Therefore,
the firm will choose to sell a positive quantity of output in the Short Run if and only if per unit price is above $2.75.
4A. Recognize that: (i) for FqqC 5
16)( it follows that 516)()( qCqMC and (ii)
25.1
800,648)(
ppD is a demand function of the “constant elasticity form” with
4525.1 . Recall that the “Inverse Elasticity Pricing Rule” states that when
maximizing profit a firm must be operating where: 1
p
MCp. Thus, applying this
rule we obtain that the firm must be setting a price for which: 5
4516
p
p. Solving for
p we obtain 16* p . This price results in sales of 275,20)16(
800,648*)(*
25.1 pDq .
4B. When charging 16* p and selling 275,20* q , this firm earns revenue of 400,324)275,20)(16(*)*)(( qp . Further, producing 275,20* q results in costs of
FFqC 880,64)275,20(*)( 516 . From here, the profit of the firm is:
FFq 520,259]880,64[400,324*)( . Clearly the firm is able to earn a positive profit if and only if 520,259F .
5A. (cells with values initially given are highlighted in yellow)
Quantity of Output
Variable Costs
Fixed Costs
Total Costs
Marginal Costs
Average Variable Costs
Average Fixed Costs
Average Total Costs
0 0 139,200 139,200
10 20,000 139,200 159,200 2,000 2,000 13,920 15,920
20 40,000 139,200 179,200 2,000 2,000 6,960 8,960
30 60,000 139,200 199,200 2,000 2,000 4,640 6,640
40 80,000 139,200 219,200 2,000 2,000 3,480 5,480
50 102,000 139,200 241,200 2,200 2,040 2,784 4,824
58 127,600 139,200 266,800 3,200 2,200 2,400 4,600
64 160,000 139,200 299,200 5,400 2,500 2,175 4,675
5B. If the firm is able to sell its output at a price of $3,000 per unit, then its Marginal Revenue is equal to $3,000 for each unit sold. From the values reported for Marginal Costs in the table above, it follows that the optimal quantity to sell in this case would be 50 units. This would give the firm Total Revenue of $150,000. But, since the firm would be incurring Total Costs of $241,200, the profit of the firm is equal to $(–91,200).
5C. If the firm is able to sell its output at a price of $5,000 per unit, then its Marginal Revenue is equal to $5,000 for each unit sold. From the values reported for Marginal Costs in the table above, it follows that the optimal quantity to sell in this case would be 58 units. This would give the firm Total Revenue of $290,000. Since the firm would be incurring Total Costs of $266,800, the profit of the firm is equal to $(23,200).
6. Recognize that the estimated value of price elasticity is within the range of “inelastic
demand.” As a result, the firm could actually increase revenue by increasing the price they charge and selling fewer units of output. Further, since Marginal Costs of Production should always be greater than or equal to zero (i.e., it should never cost less to produce more output), decreasing quantity sold will also decrease costs of production. Since Profit is generally equal to “(Total Revenues)–(Total Costs),” it follows that this change must result in greater profit (again, since it increased Total Revenues and decreased Total Costs). Thus, in general, if we observe a firm that is operating along an inelastic portion of their demand curve, we know that the firm is not maximizing profit.
7A. For 7504)( 2
1001 qqqC we have 4)()( 50
1 qqCqMC . When facing demand
of qqPD 200113)( , Total Revenue can be expressed as 2
200113)()( qqqqPqR D .
From here it follows that qqRqMR 100113)()( .
7B. To maximize profit, the firm must operate where )()( qMCqMR . From the functional
forms derived above, this requires: 413 501
1001 qq q100
39 300* q . The
optimal price of the firm is: 50.1150.113)300(13*)(* 2001 qPp D .
7C. In order to maximize Total Social Surplus, trade would have to occur exactly up to the point where )()( qPqMC D qq 200
1501 134 9200
5 q 360Eq .
7D. Note that graphically we have:
$
0
0
quantity
qqPD 200113)(
13.00
4.00
qqMR 100113)(
4)( 501 qqMC
10*)( qMC
50.11*)( qPD
360Eq300*q
300,1
600,2
c d
e
a
b
f
Total Consumers’ Surplus is represented by “Areas (e)+(f)” in the graph above. Collectively these areas are a triangle with base of 300 and height of 1.50. Thus, Total Consumers’ Surplus is equal to $225. Total Producer’s Surplus is represented by the sum of “Areas (b)+(c)” and “Area (a)” in the graph above. “Areas (b)+(c)” are collectively a rectangle with base of 300 and height of 1.50, and therefore an area of 450. “Area (a)” is a triangle with base of 300 and height of 6, and therefore an area of 900. Thus, Total Producer’s Surplus is equal to $1,350. Recall that Profit is equal to Producer’s Surplus minus Fixed Costs of Production. Thus, profit of the firm is equal to ($1,350)–($750) = $600. Finally, Deadweight-Loss is represented by “Area (d)” in the graph above. This area is a triangle with base of 60 and height of 1.50, and therefore has an area of 45. Thus, Deadweight-Loss is equal to $45.
7E. Price Elasticity of Demand is )(
)(
%
%
qPq
qP
P
Q
D
D
. For qqPD 200113)( it follows that
2001)( qPD . Thus,
q
q
q
q
qPq
qP
D
D 600,213
)(
)(
2001
2001
.
7F. To satisfy the IEPR, the firm must be operating where 1
p
MCp . From the answers
thus far we have: 23
3
5.11
105.11
p
MCp and 23
3
300,2
300
600,2
1
q
q
. Thus, we see that the
IEPR is being satisfied.
