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Intermediate Microeconomic Theory

Factor Demand/Firm Behavior

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Firm Behavior

Given its technology, we now want to develop a model of firm behavior.

What is our basic assumption about firm behavior?

Firm Behavior

Standard assumption: firms make decisions to maximize profits, or maximize total revenue minus total costs.

where q = f(x1,…,xm)

Decision process can be broken up into two parts: For any given level of output, what combination

of inputs should firm use? (Optimal Production)

Given optimal production, how much should it produce/supply? (Supply)

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Production

We will first consider the Production decision.

Key idea: Consider any level of output for firm: q If firm is producing q in the profit maximizing

way, it must be producing q using the cost minimizing process (why must this be the case?)

So, key to modeling production behavior is to think about how firms can minimize cost of producing any given level of output.

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Costs

When economists think about costs, they think much more broadly than do accountants.

Costs include not only direct costs that must be paid for, but indirect costs or “opportunity costs”

Opportunity cost - Lost revenue from failing to use an input factor for next best use.

Costs

Suppose a friend suggests you should DJ parties on Sat nights for the next month. To do so, you would have to rent a sound and light system for $1000 (which would have to be paid at the beginning of the month).

You are currently working at a coffee shop on Saturday nights 8-12 for $10/hr (for which you are paid at the end of every month). You also have $1500 in a money market account earning 1% per month.

From your perspective at the end of the month, what would have been the economic cost to you to be a DJ?

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Iso-Cost Curves

From now on, when we consider costs, we consider economic costs (meaning opportunity costs are implicitly included)

Now we want to consider the costs of different input bundles. If we again consider the simple two-input case we can think of the cost of

different input bundles via Iso-cost curves.

What is an Iso-cost curve?

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Iso-Cost Curves Iso-cost curves - all combinations of inputs that cost the

same amount. Example: Suppose input prices are w1 = $10 w2 = $20.

What would $100 Iso-cost curve look like?

How about for the $200 Iso-cost curve?

What happens to Iso-cost curves when input prices change to w1 = $20 w2 = $20?

So what is slope and interpretation of slope of an Iso-cost curve?

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Production Decision Consider a firm with a technology given by a production function

F(x1, x2) = x10.25 x2

0.25, and price of the inputs are w1 = 1 and w2 = 2. What would any given iso-quant look like? What would iso-cost curves

look like?

So how would we graphically characterize the “optimal” input bundle for this firm to use to produce 100 units of output?

How do you interpret this?

What about a different level of output, say q = 200? What if prices were w1 = 2 and w2 = 2?

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Production Decision

So firm’s decision regarding which input bundle to use to produce a given level of output is similar (but not identical) to individual’s decision regarding which bundle good he should consume to produce utility.

Individual - Chooses bundle that is on highest Indifference Curve, but is still on budget constraint for $m.

(“Utility Maximization”)

Firm – To produce q units of output, choose input bundle that is on lowest Iso-cost curve, but still is on Isoquant curve for q.

(“Cost Minimization”)

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Conditional Factor Demands

In consumer theory, choice problem over good given different prices gives demand curve for goods.

In producer theory, choice problem over different input factors given prices gives conditional factor demand curve

Denoted x1(w1, w2, q) Still the relationship between quantity

demanded (in this case of an input) and its own price.

However, it is “conditional” because it gives demand for inputs conditional on producing a given amount q.

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Conditional Factor Demand Curve

What will the conditional factor demand curve for axe handles look like for producing 100 axes if blades cost $1 each?

What will the conditional factor demand curve for Washington apples look like for producing 100 ounces of apple juice if each apple produces 2 ounces of juice and Maine apples cost $0.10 each?

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Conditional Factor Demand Curve More generally, we can derive the Conditional Factor Demand

Curve for a given input factor by choosing a given output level, then varying the price of one input while the holding prices of other inputs constant. Graphically?

How will this conditional factor demand curve change if we consider a higher level of output?

How about higher price for the other input?

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Thinking about Conditional Factor Demand Curves We can still think about things like factor demand elasticity, or

the percentage change in quantity demanded due to a percentage change in its own price.

What will factor demand elasticity generally depend on?

So which would likely have a more elastic factor demand curve---accountants in the production of tax preparation services, or medical doctors in the production of knee surgeries?

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Conditional Factor Demands Analytically

How would we derive conditional factor demand function analytically, say for a Cobb-Douglas production function:

F(x1, x2) = x1ax2

b and input prices w1 and w2?

What two conditions hold at optimal input bundle in example from above?

How do we use these to derive optimal input bundle for any given q?

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Conditional Factor Demands Analytically

So for Cobb-Douglas Technology, conditional factor demands for the two factors, conditional on producing q units, are given by the following two equations:

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Conditional Factor Demand Curve Analytically So what will be conditional factor demand curve for input x1 given

production function F(x1, x2) = x10.5x2

0.5, w1 = 2 and w2 = 8?

How about for input x2?

What happens to conditional demand for x1 as its own price rises? The price of the other input falls?

So if x1 and x2 are only inputs (i.e. no other direct or opportunity costs) and firm is a cost minimizer, how much will it cost to produce 100 units of output? How about 200? How about q units?

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Is there (Middle Class) Life After Maytag?

Describe the “economics” of the New York Times article on the changes in the factor demand for labor by Maytag.

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Is there (Middle Class) Life After Maytag?

LNewton

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q=1500q=1500

$1 million isocost

LX

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Newton FactoryFactory in City X

900

So if labor in Newton and City X cost the same, the initial situation for producing 3000 units of output would be like above, and would cost $2 million.

But cost of Labor is not the same in Newton and Monterey, so what happens?

900

$1 million isocost

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Is there (Middle Class) Life After Maytag?

LNewton

K

q=1500q=1500 q=3000

$1 million isocost

$700,000 isocost

$1.2 million isocost

LMonterey

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Newton FactoryMonterey Factory

1600900

So in example above, what happens to labor input? How much money is saved?

Besides the “economics,” what else does the article emphasize?

900

$1 million isocost (Monterey)

1000