Suppose a Cobb-Douglas Production function is given by the following:P(L, K) = 90L0.75 K0.25where L is units of labor, K is units of capital, and P(L, K) is total units that can be produced with thislabor/capital combination. Suppose each unit of labor costs $1,000 and each unit of capital costs $3,000.Further suppose a total of $480,000 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 yourbudgetary 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 youranswer to the nearest whole unit.)Max production=units

The objective of the question is to determine the optimal allocation of labor and capital to…

Answered: Suppose a Cobb-Douglas Production…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

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Cigarland is a Latin American country producing cigars. If the unit cost is 11 dollars and firms' mark up is 20 per cent, calculate the price of each cigar. Answer the question by providing just the appropriate number of dollars in the box below to one decimal place (eg 12.3). Do not enter a comma, space, letters, words or symbols (such as $). Failure to follow these instructions may result in your answer being marked as incorrect. Next page > < Previous page
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?
Consider a production function Q = (K.5 + L.5) 2 Does this production function exhibit Increasing, Constant, or Decreasing returns to scale?
The equation below is a production function, Q = (200)L + (100)K – (0.2)L2 – (0.1)K2 , where Q is output, L is labor and K is capital. What is the Marginal Product of Labor of this function?
RBW produces light sticks for one of their legendary girl groups, Kara. Suppose that RBWuses capital, K, and labor, L, to produce the light sticks. The production function is given as: Q(K,L)=2K0.75L0.51. Identify if RBW’s production function is increasing, constant, or decreasing returns to scale with a brief explanation. Also, solve for the company’s cost minimization problem by providing conditional demand functions of labor and capital, with respect to their input prices. Assume that w is the wage of labor and r is the rent cost of capital.2. Suppose that RBW is preparing for a mini-fan meet for the group’s “When I move” mini-album launch and that they have to provide 200 light sticks. The wage of labor, w, is $6.00 and the cost of capital, r, is $2.00. Determine how much labor and capital they have to use and the total cost of producing the light sticks.
Hannah and Sam run Moretown Makeovers, a home remodeling business. The number of square feet they can remodel in a week is described by the Cobb-Douglas production function Q=F(L,K) Q=10L^0.5K^0.5,where L is their number of workers and K is units of capital. The wage rate is $250 per week and a unit of capital costs $250 per week. Suppose that when initially producing 100 square feet a week, they use 10 units of capital.a. What is their short-run cost of remodeling 1,000 square feet per week? Instructions: Enter your answer as a whole number. $ b. What is their long-run cost of remodeling 1,000 square feet per week? Instructions: Enter your answer as a whole number. $
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Question 6 ▼ Suppose a Cobb-Douglas Production function is given by the following: P(L, K) = 10L0.9 K0.1 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 $100 and each unit of capital costs $700. Further suppose a total of $140,000 is available to be invested in labor and capital (combined). Units of labor, L = A) How many units of labor and capital should be "purchased" to maximize production subject to your budgetary constraint? Submit Question 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 = Question Help: Video units
The following equations represent the long-run production functions for four different technologies, where capital and labor are both variable inputs. For each function, indicate whether it exhibits increasing, decreasing, or constant returns to scale. Clearly show your derivations. (Note that in parts a and c, the exponents are decimals.) f(L,K)= 8L²K4 b. f(L,K)= L+7K c. f(L,K)= L³K d. f(L,K)= 4L+K? а. с.
How would you determine that a two-input Cobb-Douglas production function has decreasing returns to scale (DRS), increasing returns to scale (IRS) or constant returns to scale (CRS) depending on whether α1 + α2 is larger than, smaller than, or equal to one?
You are given the production function: Q(K,L)=10KαLβ What is the average product of labour, holding capital fixed at K? Simplify fully
The equation below is a production function, Q = (200)L + (100)K – (0.2)L2 – (0.1)K2 , where Q is output, L is labor and K is capital. What is the Marginal Product of Labor and capital of this function?

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