(1)
y = x1/2
(a)
Squaring,
x = y2
Total cost, C(y) = w.x = w.y2
AC(y) = C(y)/y = w.y
MC(y) = dC(y)/dy = 2w.y
(b)
Firm supply function is its MC function. So,
Firm's supply: p = MC
p = 2w.y
y = p / 2w
(c)
y = 10 / (2 x 1) = 5
Revenue (R) = p.y = 10 x 5 = 50
Cost C(y) = 1 x 5 x 5 = 25
Profit = R - C = 50 - 25 = 25
NOTE: As HOMEWORKLIB Answering Policy, 1st question is answered.
1. Let the production function be y = c. (a) Suppose the price of is w...
1. Let the production function be y=. (a) Suppose the price of x is w = 1. Find the firm's total cost curve C(s), average cost curve AC(y), and marginal cost curve MC(y). (b) Assume that p min AC(y), find the firm's supply curve y(w.p). (e) Suppose the price of y is p = 10, and the price of the input x is w = 1, calculate the firm's profit.
2. Assume the production function is y 5-30, and the price of r 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) Assume that p> min AC(y), derive the firm's supply curve y(w,p)?
2. Assume the production function is y 5-30, and the price of r 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) Assume that p> min AC(y), derive the firm's supply curve y'(w,p)?
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...
2. Assume the production function is y = 505-30, and the price of ris w = 1. (a) Derive the firm's total cost curve C(y), average cost curve AC(y), and marginal cost curve MC(y). (b) Assume that p > min AC(y), derive the firm's supply curve y(w,p)?
3. Consider the production function y= . Assume r 1. (a) Show that the production function y(x) is concave. (b) Show that the inverse production function r(y) is convex (c) The price of y is p 10. Find the firm's total product TP(x), marginal product MP(a) and average product AP(a) (d) Find the firm's value of marginal product VMP(a), and value of average product VAP(r) (e) Assume w < marVAP (x) Find the firm's input demand curve r*(w) (f) Suppose...
3. Consider the production function y=. Assume r > 1. (a) Show that the production function y(«) is concave. (b) Show that the inverse production function z(y) is convex. (e) The price of y is p= 10. Find the firm's total product TP(x), marginal product MP) and average product AP (a). (d) Find the firm's value of marginal product VMP), and value of average product V AP(x). (e) Assume w<marV AP(x) Find the firm's input demand curve r*(w). (1) Suppose...
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Consider the production function y= x^(1/2). However, assume that, for political reasons, it is not feasible to hire fewer then one unit of input. Thus, assume x>= 1. (a) Show that the inverse production function x(y) is convex. (b) The price of y is p= 10. Find the firm's marginal product MP(x) and average product AP(x). (c) Find the firm's value of marginal product VMP(x) and value of average product VAP(x). (d) Find the firm's input demand curve x*(w). (e)...
2. Assume the production function is y = 5x1/3 - 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)?