2. The Longheel Press produces memo pads in its local shop. The company can rent its equipment and hire workers at competitive rates. Equipment needed for this operation can be rented at $52 per hour, and labor can be hired at $12 per worker hour. The company has allocated $150,000 for the initial run of memo pads. The production function using available technology can be expressed as: Q=0.25K 0.25 0.75 where Q is memo pads (boxes per hour), K is capital input (units per hour), and L is labor input (units of worker time per hour). The marginal products of labor and capital are as follows: MPL = (0.75)(0.25)K 0.25-0.25 a. Construct the isocost equation. and MPK = (0.25)(0.25)K-0.750.75 b. Determine the appropriate input mix to get the greatest output for an outlay of $150,000 for a production run of memo pads. Also, compute output. c. Explain what would happen in the short-run (keeping capital fixed) to the appropriate input mix if production were changed to 1,500 units per hour. Would the input combination be different in the long-run? If so, how would it change? Explain.

2. The Longheel Press produces memo pads in its local shop. The company can rent its equipment and hire workers at competitive rates. Equipment needed for this operation can be rented at $52 per hour, and labor can be hired at $12 per worker hour. The company has allocated $150,000 for the initial run of memo pads. The production function using available technology can be expressed as: Q=0.25K 0.25 0.75 where Q is memo pads (boxes per hour), K is capital input (units per hour), and L is labor input (units of worker time per hour). The marginal products of labor and capital are as follows: MPL = (0.75)(0.25)K 0.25-0.25 a. Construct the isocost equation. and MPK = (0.25)(0.25)K-0.750.75 b. Determine the appropriate input mix to get the greatest output for an outlay of $150,000 for a production run of memo pads. Also, compute output. c. Explain what would happen in the short-run (keeping capital fixed) to the appropriate input mix if production were changed to 1,500 units per hour. Would the input combination be different in the long-run? If so, how would it change? Explain.

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

The Mini-Case "Economies of Scale at Google describes economies of scale for Google Cloud Storage. The cost function for this service is well-approximated by K C(q)-F+cq where C is total cost, F is fixed cost, c is a constant and q is output. What is marginal cost for this cost function? What are the average fixed cost, average variable cost, and average cost? Over what range of output does Google have economies of scale? The marginal cost function (MC) is The average fixed cost function (AFC) is AFC- The average variable cost function (AVC) is AVC- MC-C The average cost function (AC) is AC- (Property format your expressions using the tools in the palette. Hover over tools to see keyboard shortcuts. Eg, a fraction can be created with the character) Time Remaining: 02.09.09
Assume that C(x) is in dollars and x is the number of units produced and sold. For the total-cost function C(x)=0.01x² +0.4x + 50, find AC and C'(x) when x = 60 and Ax = 1. AC $ (Simplify your answer. Type an integer or decimal rounded to two decimal places as needed) C'(x) when x= 60 is $ (Type an integer or a decimal) per unit
Suppose a firm has the following production function Q = f(K,L) = (1/2)L(2/3)K(1/3) and a total cost function TC = wL + rK The rental cost of capital is 2 euros per hour and the labor wage is 4 euros per hour. Suppose also that in the short-run, the firm uses 8 machines in the production process. (a) Show that the firm’s short-run average cost (SRAC) is SRACK=8 = (16/Q)+ 4√? (b) Draw the SRAC curve(c) By solving the first order conditions that the global minimum of production is 4(d) Show that the firm’s long-run average cost (LRAC) is 12. Hint: Start by obtaining the firm’s long-run expansion path(e) Draw both the SRAC and the LRAC and explain why the SRAC is always equal or above the LRAC.
Cost minimization when output is known and total costs are unknown. A factory that you are managing has an hourly production process that can be represented by the following Cobb Douglas Production function: Q = 2K0.50L 0.5 The price of one unit of capital per hour is $20 and the price of one unit of labour per hour is $20. You have been instructed to produce 200 units per hour or Q = 200. Find the optimal amount of labour and capital that you will be using, and compute the total cost.
You are the owner of a small company that makes laptops at the price of $550. Your variable cost of production is 0.75q, such that q represents number of laptops made. If you were going to build a second company that has the following variable cost for 0.3q. What is the maximum fixed cost that you are okay with paying for this new company?
4. Ikea Inc., a home remodeling business. The number of square feet they can remodel in a day is described by the Cobb-Douglas production function Q= F (L,K)= 4K5L0.5 where L is their number of workers and K is units of capital. The wage rate is $5 a day, and a unit of capital costs $20 a day. What is their minimum cost input combination for remodeling (Q=200) 200 square feet a day? What is the total minimum cost level? (15p)
A firm estimates its production function as Q = -2.4 + 20*L -.5*L2 + 30*K -1.00*K2 + 15*F -.3*F2. Total cost is TC = $2*L + $2.5*K + $1.75*F. The firm wishes to produce 400 units of output. Use Excel to find the cost minimizing amounts of L, K and F. How much F (Fuel) should the firm use?
A factory that you are managing has an hourly production process that can be represented by the following Cobb Douglas Production function: Q=10KL. The price of one unit of capital per hour is $20 and the price of one unit of labour per hour is $20. You have been instructed to produce 100 units per hour or Q-100. Find the optimal amount of labour and capital that you will be using, and compute the total cost.
Answer the question on the basis of the following cost data. Average Fixed Average Variable Output Cost Cost 1 $ 50.00 $ 100.00 2 25.00 80.00 3 16.67 66.67 4 12.50 65.00 5:35 5 10.00 68.00 6 8.37 73.33 7 7.14 80.00 8 6.25 87.50 The marginal cost of the sixth unit of output is Multiple Choice О $440.00. $8.37.
1. A firm estimates its production function as Q = -2.4 + 20*L -.5*L< + 30*K -1.00*K2 + 15*F -.3*F<. Total cost is TC = $2*L+ $2.5*K + $1.75*F. The firm wishes to produce 400 units of output. Use Excel to find the cost minimizing amounts of L, K and F. How much F (Fuel) should the firm use? A.F=7.90. B.F=9.58. C.F=10.75. D.F=12.63. E. F=14.88.
suppose a company has two production facilities with two different TC functions. in facility A total costs are given by $600,000+0.4Q^2 in facility B total costs are given by $300,000+0.5Q^2 The firm needs to produce 900 units how many units should they produce in facilities a and b to minimize total costs
A firm produces plastic bins using labor (measured in man-hours) and capital (measured in machine-hours), according to the production function Q = f(L,K) = LK, where Q is the number of plastic bins produced. Suppose that the cost of labor is $20 per worker-hour and the cost of capital is $10 per machine-hour. What is the cost minimizing input combination if the firm wants to produce 28,800 plastic bins? Hint: The marginal products are MP, = K and MPg = L.