PDF Chapter 8 Cost Functions Done - University of Tennessee

Chapter 8

Costs Functions

The economic cost of an input is the minimum payment required to keep the input in its present employment. It is the payment the input would receive in its best alternative employment. This cost concept is closely related to the opportunity cost concept (not talking about accounting costs).

We usually assume that inputs are hired in perfectly competitive markets. The firm can get all the input it wants without affecting prices. The supply curve for an input is horizontal at the prevailing price.

w

Supply of the input = price of the input.

Firm's demand for the input

L

Total Cost, Revenue, and Profit

? Total cost = C = wL + vK (with only 2 inputs, capital and labor)

? TR = pq (with only 1 output) ? Then, economic profit is:

pq wL vK pf(K,L) wL vK

? Thus, economic profit is simply a function of K and L, given that all prices (p, w, and v) and technology are fixed.

Cost Minimizing Input Choices (for given q)

? Assume for now that output has been determined to be q0 and the firm wishes to minimize its cost. That is, the firm must choose a specific point on the q0 isoquant.

K q0

L

? Cost will be minimized by choosing the point

where RTSLK (-slope of isoquant) equals the ratio of input prices (w/v). This happens when the rate

of substitution in production equals the rate of

substitution in the market.

FOC

Min: C = wL + vK

is the increase in C

st: q0 = f(K, L) or q0 ? f(K, L) = 0 when q0 increases by

= wL + vK + (q0 ?f(K, L))

one unit. is marginal cost, MC.

w f 0

L

L

The SOC require diminishing

v f 0

K

K

q0

f (K, L)

0

RTSLK or q=f(K, L) strictly quasiconcave or K = f(L,q0) strictly convex.

Then

w v

f f

L K

MPL MPK

RTSL,K

dK dL

So, RTSLK should equal w/v for the minimum cost combination of inputs, or the slope of the

isoquant (dK dL) equals the slope of the isocost line (w v).

MPL MPK 1 w v

the marginal product per dollar

spent is equal for all inputs.

Also, = marginal cost is the inverse of the above,

w v MC. MPL MPK

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