Question

Use profit-maximization and revealed choices by firms to show the law of supply. Be sure to define what is meant by “the law of supply”? How would the above result change if a firm faced a cost of (q1 − q2)^2 if it changed output from q1 to q2 after a price change.

Answer 1

ANSWER:

GIVEN THAT:

THE LAW OF SUPPLY:

If a firm faced a cost of (q,-q2)2

1. Take a hypothetical production function Q = L1/2 + K1/2

there are fixed prices (P, w, r MRTS = w/r

MRTS = MPL/MPK = (1/2)L^(-1/2)/(1/2)K^(-1/2) = (K/L)^(1/2)

2. At the optimum mix we have (K/L)^(1/2) = w/r

K/L = (w/r)^2, K = L(w/r)^2

function of production

Q = L^1/2 + K^1/2

Q = L^1/2 + K^1/2

Q = L^1/2 + (L(w/r)^2)^1/2

L = (Qr/(w + r))^2

K =  (Qw/(w + r))^2

3. conditional demand functions for labor and for capital on firms.

function of total coast

C = wL + rK

C = w*(Qr/(w + r))^2 + r*(Qw/(w + r))^2

C = Qwr/(w + r)

4. labor and capital paymnt VMPL = w and VMPK = r

5. This gives P*(1/2)L^(-1/2) = w and P*(1/2)K^(-1/2) = r

L = (P/2w)^2 and K = (P/2r)^2

A firm’s supply function is given as

Q = L^1/2 + K^1/2

Q = ((P/2w)^2)^1/2 + ((P/2r)^2)^1/2

Q = ((r + w)/2rw)P

6. the supply curve is positive relation between quantity an price plied.