An entrepreneur owns a factory with two plants that produce the same skateboards but differ in the amount of capital and Labor in them. They are both represented by a simple Cobb- Douglas production function without a technology component. Plant 1 has K1=1 and Plant 2 has K2=4 while w=$20 and v=$20. 1-Write both production functions and derive the respective MPL of each one. If the entrepreneur wishes to minimize Short-Run total cost: 2-How would labor and output be allocated between the two plants and why? 3-Derive the short-run Total Cost, Average Cost and Marginal Cost Functions.

An entrepreneur owns a factory with two plants that produce the same skateboards but differ in the amount of capital and Labor in them. They are both represented by a simple Cobb- Douglas production function without a technology component. Plant 1 has K1=1 and Plant 2 has K2=4 while w=$20 and v=$20. 1-Write both production functions and derive the respective MPL of each one. If the entrepreneur wishes to minimize Short-Run total cost: 2-How would labor and output be allocated between the two plants and why? 3-Derive the short-run Total Cost, Average Cost and Marginal Cost Functions.

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)

14th Edition

ISBN:9781305506381

Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Chapter7: Production Economics

Section: Chapter Questions

Problem 9E

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This question illustrates the argument on p.114 of the book. A and B own neighboring properties. Beneath their properties is a common well that contains 200 units of oil. The cost to A of extracting oil from the well in period t depends on the number of units of oil in the well at the beginning of the period t, ut, and the number of units of oil A extracts in period t, xAt ; specifically, the average cost of extraction for A per unit in period t is xAt /ut. The analogous cost function for B is xBt/ut. The market price of a barrel of oil is 1, there are two periods (t = 1, 2), and the discount rate is zero. The oil is a common property resource. a) (2) Suppose that A and B "unitize" and cooperatively decide how much oil to extract, and split the profit between them. The jointly profit-maximizing policy is that each extracts 50 units of oil from her well in each of the first two periods, after which the well is dry. How much discounted profit will A and B each make? b) (2) Suppose…
Suppose you own a small business. Last month, your total revenue was $8,800. In addition, you paid $3,500 in monthly rent for office space, $300 in monthly rent for equipment, $2,500 to your workers in wages for the month, and $1,900 for the supplies you used that month. If you correctly determine that your economic profit last month was $200, then it must be true that your implicit costs are $3,600 per month. your implicit costs are $600 per month. your implicit costs are $400 per month. your implicit costs are $1,800 per month.
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A firm has a production function of q=2(LK), where the L represents hours of labor, K represents hours of machine usage and q represents the hourly production volume. Currently the price of labor is $20 per hour and the price of capital is $40 per hour. a. When the production level is at 40,000 units, use the LaGrange process to determine how much they should spend on labor and capital. b. If the purchasing agent requests an additional unit (40,001st unit), what is the minimum price you should charge on that specific unit? (Note: determine this without re-solving the Lagrange problem itself.)
Q3, A firm operates with the following Cobb-Douglas production function where Q is output, L is labor hours per week, and K is machine hours per week. Cobb-Douglas Production Function: Q = 5(L1/3K2/3) The firm intends to produce 5,000 units of output per week by contracting employees for $40 per hour and renting machinery for $10 per hour. Determine the cost minimizing combination of labor and capital for the firm. Based on your solution in part (a), calculate the firm’s total cost of producing 5,000 units of output per week.
You are a manager at Glass Incorporated—a mirror and window supplier. Recently, you conducted a study of the production process for your single-side encapsulated window. The results from the study are summarized in the following table and are based on the 8 units of capital currently available at your plant. Each unit of labor costs RM 60, each unit of capital is RM 20, and your encapsulated windows sell for RM 12 each. Labor L Capital K Output Q Marginal Product of Labor MPL Average Product of Labor APL Average Product of Capital APK Value Marginal Product of Labor VMPL 0 8 0 1 8 10 2 8 30 3 8 60 4 8 80 5 8 90 6 8 95 7 8 95 8 8 90 9 8 80 10 8 60 11 8 30…
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Assume that Donnell Corp. is currently producing 500 units of output per period, using 25 units of labor and 20 units of capital. Values for the marginal product of each input and the prices of the inputs are as follows: MPK = 100, MPL = 200, w = 2, and r = 3. Given the information above, which of the following is true? a. The firm is currently using the optimal levels of capital and labor. b. The firm should increase labor and reduce capital usage. c. The firm is not using the optimal levels of capital and labor, and it is impossible to determine the optimal levels from the given information.
Suppose the joint cost function of a firm producing two products X and Y is given by C = 250X2 + 120Y2. Assuming that output of the two products is restricted at 4144. Using Lagrangian multiplier technique find the amounts of X and Y that will minimize cost and compute this cost. Also examine the cost implications of changing this optimal combination so as to produce equal amounts of both products.
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A small bank is trying to determine the number of tellers to employ. The total cost of employing a teller is $100 per day, and a teller can serve an average of 160 customers per day. On average, 210 customers arrive per day at the bank, and both service times and interarrival times are exponentially distributed. If the delay cost per customer day is $200, how many tellers should the bank hire?
CAN YOU ANSWER QUESTIONS 1 & 2 FOR ME? Suppose that you are the manager of a company that vaccinates human beings for biological diseases. Your company uses two inputs to produce vaccinations: physicians and laboratories. However, this is a short-run analysis where physicians are variable but laboratories are fixed. Suppose that each physician costs $500 per day (for an annual salary of about $175,000) and the daily cost for the laboratory is $1,500 (for rental cost of about $547,500 per year). In the short run, your company has 1 laboratory. The following table presents potential daily production levels with requisite input combinations. Physicians Laboratories Vaccinations (Q) TC TFC TVC MC ATC AFC AVC 0 1 0 1500 1500 0 - - - - 3 1 1 3000 1500 1500 1500 3000 1500 1500 5 1 2 4000 1500 2500 1000 2000 750 1250 6 1 3 4500 1500 3000 500 1500 500 1000…