Chapter 6: Firms and Production

• Firms (businesses) organize production of goods and services for sale in markets

• Firms take many forms from sole proprietorships (like ma and pa grocery stores) to giant multi-national corporations

• In corporations, the management and ownership of the firm are separate

• We ignore such complications and assume firms are started and run by a manger/owner called an entrepreneur

We assume entrepreneur is motivated by economic profit ()

• Economic profit () is equal to revenue (R) minus the economic cost of doing business (C)

• Revenue is equal to price times quantity of goods sold (R=P·Q)

• Economic cost is the opportunity cost of all inputs (factors of production) used by the firm

• Inputs (factors of production) are converted into outputs (goods and services that can be sold) according to a technology that can be represented by a production function

Production Function

• Summarizes a technologically efficient relationship (no waste) between factors of production and outputs

• In simplest case, a single output q is produced using quantities of two factors of production labor (L) {or materials (M)} and capital (K)

• The mathematical representation is q=f(L,K) where q is the maximum quantity of output that can be produced with the given quantities of labor and capital

Production horizon (Short run, Long run)

• In the short run, a firm makes production decisions constrained by its production function and the inability to vary the quantity of at least one factor of production

• Common to assume that one factor of production is variable (usually L or M) and the other factor of production is fixed (usually K)

• Thus, the short-run production function is written

( , )q f L K F L

Properties of the Short-run Production Function

• Total product increases with increases in the variable factor (up to a point)

• Marginal product (MPL= Δq/ΔL) is the increase in output from an extra unit (small amount) of variable factor

• Law of diminishing returns: At some level of variable factor, the marginal product of the variable factor must decline (because you are adding more and more of it to a fixed factor)

• Average product (APL= q/L) is increasing if marginal product is greater and decreasing if marginal product is less.

Table 6.1 Total Product, Marginal Product, and Average Product of Labor with Fixed Capital

Figure 6.1 Production

Relationships with Variable

Labor

**Note relationship between marginal and

average product curves

The range where MPL is increasing can exist but need not exist

• The production function in Fig. 6.1 is a logistic function (too complicated for problem sets)

• Consider the square root production function

• MPL is declining (diminishing returns is global) and is less than APL so APL is declining too

2 if 4q K L L K

1/ and 2 /L LMP L AP L

q

L

MPL

APL

Approximate marginal and average product curves for the square root production function with capital fixed

Production function with two variable factors

• If only factors are labor and capital, this corresponds to a long-run production horizon

• Challenge of plotting three variables (q, L, K) on a two dimensional graph

• Use same trick as we did with indifference curves—in this case isoquants

• An isoquant plots the combinations of labor and capital sufficient to produce a given quantity of output

• Isoquant maps have same properties as indifference cuve maps

Find the isoquant for q=24

Figure 6.2 Family of Isoquants

Shapes of isoquants represent substitutability of the factors of production

• If two factors are perfect substitutes, the isoquants are straight lines (Idaho potatoes and Washington potatoes for making potato salad)

• If two factors are perfect complements (no substitutability) the isoquants are right angles (Cereal boxes and cereal for making boxes of cereal)

• The general case was that shown in figure 6.2• Assignment: Read application on page 163 to

see how you can get isoquant from substituting difference processes of making something (SIC)

Figure 6.3a Substitutability of Inputs

Figure 6.3b Substitutability of Inputs

Application (Page 164) Semiconductor Integrated Circuit Isoquants

Substituting factors of production

• The slope of an isoquant measures how much you can substitute one factor for another at the margin

• The absolute value of the slope is called the marginal rate of technical substitution (MRTS)

• The law of diminishing returns implies that the MRTS of the increasing factor declines

Figure 6.4 How the Marginal Rate of Technical Substitution Varies Along an Isoquant

MRTS=minus ΔK/ΔL

The MRTS and the marginal product of the factors

• Along an isoquant, output is constant so

MPL×ΔL+MPK×ΔK=0

• Rearrange to get:

• As L increases and K decreases along the isoquant, MPL falls and MPK rises so MRTS falls

L

K

MPKMRTS

L MP

Returns to scale

• Diminishing returns is exhibited when one factor is increased while another is fixed

• When all factors are increased (or decreased) in the same proportion, we have a change in scale

• If the production process is replicable, we should expect to see constant returns to scale (CRS)

• If the production function has CRS, increasing L and K by x% would increase q by x%

• If q increases by more or less than x%, the production function exhibits increasing returns to scale (IRS) or decreasing returns to scale (DRS)

A simple production function is the Cobb-Douglas form

• Three parameters: A, , and

• The Cobb-Douglas production function has CRS if +=1

• The Cobb-Douglas production function has increasing (decreasing) returns to scale if +

• If ==½, we have the square root production function

q A L K

Technological change

• Technological change can be represented by changes in the parameters of the production function.

• For example, an increase in A in the Cobb-Douglas production function would allow for more output for the same quantities of factors

• This would be a factor-neutral technological improvement

• Combining changes in A, and can represent factor-biased technological improvements