Answered: A firm's production function is given…

Micro Economics For Today

10th Edition

ISBN:9781337613064

Author:Tucker, Irvin B.

Publisher:Tucker, Irvin B.

Chapter7: Proudction Costs

Section: Chapter Questions

Problem 3SQP

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a= min[x,y]^(1/2) a)Draw isoquants for a = 1, a = 4 and a = 9. b)What kind of returns to scale does the production function have? c)The price of x is p_x = 1 and of y p_y = 2. Calculate the cost function. d)Rent is $ 400, calculate average and marginal costs.
A firm can manufacture a product according to the production function Q = F(K, L) = K0.5L0.5. (a) What is the average product of labor, APL, when the level of capital is fixed at 36 units and the firm uses 16 units of labor? (b) What is the marginal product of labor, MPL, when capital is fixed at 36 units? (c) Suppose capital is fixed at 36 units. If the firm can sell its output at a price of $100 per unit of output and can hire labor at $40 per unit of labor, how many units of labor should the firm hire in order to maximize profits?
A production function is represented by P=f(L), where L is labour. As input L increases, the total output will increase but what will happen to marginal product? Can marginal product be zero? if so, what it mean
A firm produces output according to the production function Q = F(K, L) = 4K + 8L.A. If the wage rate is $60 per hour and the rental rate on capital is $20 per hour, what isthe cost-minimizing input mix for producing 32 units of output?
Craig and Javad run a paper company. Each week they need to produce 1,000 reams of paper to ship to their customers. The paper plant's longrun production function is Q = 4KL, where Q is the number of reams produced, K is the quantity of capital rented, and L is the quantity of labor hired. The weekly cost function for the paper plant is C = 20K + 4L, where C is the total weekly cost. (a) What ratio of capital to labor minimizes Craig and Javad's total costs? (b) How much capital and labor will Craig and Javad need to rent and hire in order to produce 1,000 reams of paper each week? (c) How much will hiring these inputs cost them?
A firm has the production function Q(L, K) = √K + 2√L. The price of one unit of capital is R> 0, and the price of one unit of labor is W> 0. Which of the following statements is correct? The production function can be represented by a CES production function [aL + bKº] for suitable values of a, b and p. The production function has increasing returns to scale. The marginal rate of technical substitution is MRTS (L, K) = 2√L VR OfW= R. the fi rm's demand for labor is four times the demand for capital.
Please no written by hand and no emage Consider the production function q = min{ l /2 , k/ 3 }. Where l is labour, k is capital and q is output. What is the associated cost function if l costs w per unit and k costs r per unit.
a) A firm operates according to the following production function: q(K,L)=100 KS LOS. The price of capital is r=$15/unit and the price of labor is w=$60 per unit. The firm currently operates with KSR-100 units of capital and wants to produce qs 4000 units of output. How much labor does the firm need to hire and what is the total cost of producing the 4000 units?
A company chooses the two inputs *1 duce its output y. f(x1, x₂) y = and 2 to pro- The production function is given as 1/2 1/2, and input prices are ₁ = 80 and 4x1x2 = w220. The firm also has fixed costs of F = 100. a) Find the formula for the firm's isoquants, and sketch the isoquant for y = 16 in a diagram. b) Compute the firm's optimal input combination (x(16),x(16)), and illustrate it in your diagram in a). Explain your steps. What are the firm's costs of producing 16 units? c) Find the firm's cost function C(y). Explain what you are doing.
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). (d) Where does the SMC curve intersect the SAC curve? Explain why the SMC curve will always intersect the SAC curve at its lowest point Suppose 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…
Asap A firm has the following linear production function: Q = 6K + 9L The firm currently owns 10 units of capital (K) and hires 30 workers (L). A) What is the marginal product of labor? B)What is the marginal product of capital?
The production function of a firm is f : R² → R, (L, K) + 10L + 16K – 2L? – K?, and the per unit costs of the quantities of labor input L and capital input K are 4 and 2 dollars, respectively. The firm wants to maximize its production of output subject to the total cost of production not exceeding 20 dollars. The firm can only employ non-negative quantities of labor and capital. (a) Write the firm's problem as an optimization problem with inequality constraints. (b) Identify any points in the constraint set that violate the non-degenerate constraint. qualification for the problem in (a). (c) Construct the Kuhn-Tucker Lagrangian by defining L(L, K, X) for the probļem in (a). (d) List the Kunh-Tucker first-order conditions for the problem in (a). (e) Solve the first-order conditions from (d) to find the critical points of the Lagrangian. (f) Justify that the problem in (a) is a concave program and conclude with the values of labor and capital that solve the firm's problem. (g) Based on…

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A firm's production function is given as: q = K1/3 L1/3 where the rental rate (price) of capital r = N$60 and wage rate w = N$54 What is the cost-minimizing capital to labor ratio?