Suppose a Cobb-Douglas Production function is given by the following: P(L, K) = 70L0.9K®1 where L is units of labor, K is units of capital, and P(L, K) is total units that can be produced with this labor/capital combination. Suppose each unit of labor costs $1,000 and each unit of capital costs $7,000. Further suppose a total of $2,800,000 is available to be invested in labor and capital (combined). A) How many units of labor and capital should be "purchased" to maximize production subject to your budgetary constraint? Units of labor, L - Units of capital, K - B) What is the maximum number of units of production under the given budgetary conditions? (Round your answer to the nearest whole unit.) Max production units

Suppose a Cobb-Douglas Production function is given by the following: P(L, K) = 70L0.9K®1 where L is units of labor, K is units of capital, and P(L, K) is total units that can be produced with this labor/capital combination. Suppose each unit of labor costs $1,000 and each unit of capital costs $7,000. Further suppose a total of $2,800,000 is available to be invested in labor and capital (combined). A) How many units of labor and capital should be "purchased" to maximize production subject to your budgetary constraint? Units of labor, L - Units of capital, K - B) What is the maximum number of units of production under the given budgetary conditions? (Round your answer to the nearest whole unit.) Max production units

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Assume a Cobb-Douglas production function of the form: q=10L0.98K0.88 What type of returns to scale does this production function exhibit? In this instance, returns to scale equal. (Enter a numeric response using a real number rounded to two decimal places.)
Suppose that a firm's production function is Q = F(L) = -1L³-30L² + 5,000L. Its marginal product of labor is MPL = -3L2-60L +5,000. a. At what amount of labor input are the firm's average and marginal product of labor equal (other than at L = 0)? Instructions: Enter your answer as a whole number. units. b. Confirm that the average and marginal product curves satisfy the relationship discussed in the text. When the amount of labor input is less than the quantity identified in your answer above, the marginal product of labor is greater than the average product of labor. When labor is greater than the amount identified above, the marginal product of labor is less than the average product of labor.
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Consider the following production function of DVDS: Q = K0.5L 0.5, where Q represents DVDS (boxes per hour), K denotes capital input (units per hour), and L denotes labour input (units of worker time per hour). The unit cost of capital and labour are $40 and $20, respectively. a) What is the optimal input ratio of labour and capital for the production? b) Determine the appropriate input mix to produce 800 boxes of DVDS. Compute the cost of production. c) Suppose the government decided to offer a subsidy that would make the cost of labour $15. What is the optimal input mix to produce the same level of output, and the new cost of production? Also, compute the substitution effect in the employment of labour.
Suppose the production function for widgets is given by: Q = f (K, L) = 2 ∗ KL − K2/2 − L2/2 (a) Suppose L=5 (is fixed), derive an expression for and graph the total product of capital curve (the production function for a fixed level of labor) and the average productivity of capital curve. (b) At what level of capital input does the average productivity reach a maximum? How many widgets are produced at this point? (c) Again, assuming L=5, derive an expression for and graph the MPK curve. At what level of capital input does MPK =0? (d) Does this production function exhibit constant, increasing or decreasing returns to scale?
uppose a Cobb-Douglas Production function is given by the following:P(L,K)=60L^0.8K^0.2where LL is units of labor, KK is units of capital, and P(L,K) is total units that can be produced with this labor/capital combination. Suppose each unit of labor costs $900 and each unit of capital costs $3,600. Further suppose a total of $900,000 is available to be invested in labor and capital (combined).A) How many units of labor and capital should be "purchased" to maximize production subject to your budgetary constraint?Units of labor, LL = Units of capital, KK = B) What is the maximum number of units of production under the given budgetary conditions? (Round your answer to the nearest whole unit.)Max production = units
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