A firm producing hockey sticks has a production function given byq = 2VklIn the short run, the firm's amount of capital equipment is fixed at k = 100. The rental rate for k isr = 5, and the wage rate for r = $1, and the wage rate for l is w = $4.(a) Calculate the firm's short-run total cost curve. Calculate the short-run average cost curve.(b) What is the firm's short-run marginal cost function? What are the SC, SAC, and SMC for thefirm if it produces 25 hockey sticks? Fifty hockey sticks? One hundred hockey sticks? Twohundred hockey sticks?(c) Graph the SAC and the SMC curves for the firm. Indicate the points found in part (b).(d) Where does the SMC curve intersect the SAC curve? Explain why the SMC curve will alwaysintersect the SAC curve at its lowest pointSuppose now that capital used for producing hockey sticks is fixed at ki in the short run.(e) Calculate the firm's total costs as a function of q, w, r, and k1.(f) Given q,w,and r, how should the capital stock be chosen to minimize total cost?(g) Use your results from part (f) to calculate the long-run total cost of hockey stick production.(h) For w = $4, r = $1, graph the long-run total cost curve for hockey stick production. Showthat this is an envelope for the short-run curves computed in part (e) by examining values ofki of 100, 200, and 400.2.

A firm producing hockey sticks has a production function given by q = 2vkl In the short run, the firm's amount of capital equipment is fixed at k = 100. The rental rate for k is r = 5, and the wage rate for r = $1, and the wage rate for l is w = $4. (a) Calculate the firm's short-run total cost curve. Calculate the short-run average cost curve. (b) What is the firm's short-run marginal cost function? What are the SC, SAC, and SMC for the firm if it produces 25 hockey sticks? Fifty hockey sticks? One hundred hockey sticks? Two hundred hockey sticks? (c) Graph the SAC and the SMC curves for the firm. Indicate the points found in part (b). 2.

A firm producing hockey sticks has a production function given by q = 2vkl In the short run, the firm's amount of capital equipment is fixed at k = 100. The rental rate for k is r = 5, and the wage rate for r = $1, and the wage rate for l is w = $4. (a) Calculate the firm's short-run total cost curve. Calculate the short-run average cost curve. (b) What is the firm's short-run marginal cost function? What are the SC, SAC, and SMC for the firm if it produces 25 hockey sticks? Fifty hockey sticks? One hundred hockey sticks? Two hundred hockey sticks? (c) Graph the SAC and the SMC curves for the firm. Indicate the points found in part (b). 2.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

Given a firm's cost function C = F(x) = ax² +bx + d: Find the firm's Average cost funetion (A(x) and Marginal cost function M(x). O Is C(x) more appropriatc as a long-run or short-run cost function? Explain. Determine whether the Marginal cost function is strictly monotonic for a> 0, b>0, and d> 0. Does this finction have an inverse for economically meaningful values of x? If yes, find dx/dM. If not, show/explain what restriction would be necessary for inverse to exist. a. b. c. d.
Emma sells hot chocolate outside of Yankees baseball games. They have two inputs in the production of hot chocolate: (hot chocolate mix (x1, measured in kg) and labour (x2, measured in hours. The production function for hot chocolate (in liters) is: f (x1 , x2) = (x1)1/3(x2)1/3 A) Does this firm have constant, increasing or decreasing returns to scale? The cost of hot chocolate mix is w1, and the cost of labour is w2. If Emma produces "y" liters of hot chocolate the cheapest way possible, then B) How many kilograms of hot chocolate mix would they use? C) How many hours of labour? D) What is the cost function of producing this much hot chocolate?
Consider the following short run cost function: TC = 4Q³ - 24Q² + 16Q + 100 Derive the expressions for marginal cost and average total cost. What can we infer about the range of output over which production shows increasing returns to labor and diminishing returns to labor?
If a firm has the production function q = f(L, K) = L + 2K, then its technology exhibits: constant returns to scale increasing returns to scale None of the above. decreasing returns to scale increasing marginal product
Question 4: Marginal and Average Cost curves Suppose the cost function is given by C(Q)= Q²-2Q +16. a) Find the marginal cost function b) Find the average cost function c) Find the quantity where the MC cost and the AC cost curve intersect
Suppose a firm with a production function given by Q = K0.4L0.6 produces 100 units of output. The firm pays a wage of $20 per units and pays a rental rate of capital of $40 per unit. (Note: MPL = 0.6K0.4L-0.4 and MPK = 0.4K-0.6L0.6 ) What is the minimum cost of producing 100 units of output?
A firm’s short-run production function is in the form of q = aLK +(bL^2)K −(cL^3)K , wherea, b, c > 0 are parameters. K is a constant. (a) Derive the marginal product of labor.(b) Find the level of L, expressed in terms of the parameters, at which the law ofdiminishing marginal product kicks in.
A farm producing wheat has the following production function Q = 4L + 3K. Does the above function exhibit increasing, constant, or decreasing returns to scale? Prove and explain your answer.
A firm has the following Cobb-Douglas production function: q=(L^α)(K^1-α)0<α < 1 is a parameter. Suppose in the short run K = 1. The rental rate of a unit of K is $10, and the wage rate of a unit of L is $20.(a) Derive the marginal cost of the firm (expressed in terms of α and q).(b) Derive the average variable cost of the firm (expressed in terms of α and q).(c) Derive the cost function of the firm.
M1
Suppose a firm’s total cost curve is TC = 50Q2 + 10Q + 800 and marginal cost is MC = 100Q + 10. Find the output level that minimizes average total cost and average variable cost, respectively.