Question

Questions 1-4

mize profit Therefore for any he firm will produce Y = U. 1 75 the firm by setting price equa ginal cost, which gives p = MC() = 3(y - 10). for y as a function of p leads to y(p) = 10 + p/3. Solving this equation for Exercises 1. Let the Let the production function be y=r1/2 (b) Suppose the price of ris Show that the production function y(r) is concave. ose the price of .r is w = 1. Find the firm's total cost curve C(y), average cost curve AC(y), and marginal cost curve MC(y). (c) Find the firm's supply curve y* (p). (d) Suppose the price of y is p = 10. Calculate the firm's profit. 2. Assume the production function is y = 5x13 - 30, and the price of x is w = 1. (a) Derive the firm's total cost curve C(y), average cost curve AC(y), and marginal cost curve MC(y). (b) What is the firm's supply curve y* (p)? 3. Consider the production function from question 1 above, y = x/2. However, assume that, for political reasons, it is not feasible to hire fewer than one unit of input. Thus, assumer 1.

Answer 1

(1)

y = x^1/2

(a)

dy/dx = (1/2) / x^1/2 = (1/2).x^-1/2

d²y/dx² = d/dx(dy/dx) = - (1/2).(1/2).x^-3/2 = - (1/4).x^-3/2

Since x > 0, [- (1/4).x^-3/2] > 0, which means that the function is concave.

(b)

Since y = x^1/2,

x = y²

Total cost: C(y) = w.x = w.y²

AC(y) = C(y)/y = w.y

MC(y) = dC(y)/dy = 2w.y

(c)

Firm's supply function is its MC function. So, Firm supply curve:

p = 2w.y

y = p / 2w

(d)

Revenue (R) = p.y = 10y

Profit = R - C(y) = 10y - w.y²

NOTE: As HOMEWORKLIB Answering Policy, 1st question is answered.