Suppose that the output Q (in units) of a certain company is Q = 75K¹/3-2/3, where K is the capital expenditures in thousands of dollars and L is the number of labor hours.Find aQ/ƏK when capital expenditures are $1,331,000 and the labor hours total 2197. (Round your answer to the nearest whole number.)aq/ək =units per thousand dollarsInterpret aQ/ƏK.If labor hours remain at 2197 and K increases by $1000, Q will increase aboutunits.Find aQ/aL when capital expenditures are $1,331,000 and the labor hours total 2197. (Round your answer to the nearest whole number.)ƏQ/ƏL =units per labor hourInterpret aQ/ƏL.If capital expenditures remain at $1,331,000 and L increases by one hour, Q will increase aboutunits.

Suppose that the output Q (in units) of a certain company is Q = 75K¹/32/3, where K is the capital expenditures in thousands of dollars and L is the number of labor hours. Find aQ/Ək when capital expenditures are $1,331,000 and the labor hours total 2197. (Round your answer to the nearest whole number.) aq/ək = units per thousand dollars Interpret ƏQ/ƏK. If labor hours remain at 2197 and K increases by $1000, Q will increase about units. Find aQ/aL when capital expenditures are $1,331,000 and the labor hours total 2197. (Round your answer to the nearest whole number.) aq/al = units per labor hour

Suppose that the output Q (in units) of a certain company is Q = 75K¹/32/3, where K is the capital expenditures in thousands of dollars and L is the number of labor hours. Find aQ/Ək when capital expenditures are $1,331,000 and the labor hours total 2197. (Round your answer to the nearest whole number.) aq/ək = units per thousand dollars Interpret ƏQ/ƏK. If labor hours remain at 2197 and K increases by $1000, Q will increase about units. Find aQ/aL when capital expenditures are $1,331,000 and the labor hours total 2197. (Round your answer to the nearest whole number.) aq/al = units per labor hour

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 7E

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Firm ABC has estimated that it has the following production function: Q = 1.5LK – 0.3L2 – 0.15K2 Labor (L) has a price of €60 and capital (K) has a price of €75. ABC wants to maximize the production with a total cost of €2025. (a) Determine the quantities of labor and capital the firm should use. (round results to 2 decimal places) (b) What quantity of output will be produced at the optimal combination of factors of production?
Q2. The economist for the ABC Truck Manufacturing Corporation has calculated a production function for the manufacture of their medium-size trucks as follows: Q = 1.3*(L^0.75)*(K^0.3) Where Q is the number of trucks produced per week, L is the number of labor hours per day and K is the daily usage of capital investment. 1. Does the equation exhibit increasing, constant or decreasing returns to scale? Why? 2. Calculate the marginal product of labor and marginal product of capital using the below data? 3. How many trucks will be produced per week with the following amounts of labor and capital? Labor Capital 100 50 120 60 150 75 200 100 300 150
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The per-unit cist of an item is its average total cost=(=total cost/quantity). Suppose that a new cell phone application costs $100,000 to develop and only $0.70 per unit to deliver to each cell phone customer. What will be the per-unit coat of the application if it sells 100 units? What will be the per-unit coat of the application if it sells 1,000 units? What will be the per-unit cost of the application if it sells 1 million units?
Suppose you run a factory whose short-run production function is given by f (L) = 180L² – 3L³. (a) Find mathematical expressions for the total product of labor, the average product of labor and the marginal product of labor. (b) On two separate axes, graph TPL, APL, and M PL. The diagrams do not need to be scale, but be sure they are internally consistent. In other words, make sure that all relevant relationships between the three lines are correct. If you have trouble figuring out what the graph looks like, feel free to use a graphing calculator or an online graphing tool to find the basic shape. Find the quantity of labor associated with each of the following points and label it on your diagram: (i) the maximum value of TPL, (ii) the maximum value of APL, (iii) the maximum value of MPL. (c) For what values of L does the production function exhibit each of the following: i. increasing marginal labor productivity ii. diminishing marginal labor productivity iii. negative marginal labor…
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Suppose the production function for widgets is given by q=kl -0.8k²-0.21² where q represents the annual quantity of widgets produced, k represents annual capital input, and I represents annual labor input. Suppose k = 10; at what level of labor input does this average productivity reach maximum? (please put your answer in numerical values with no comma or decimal place). How many widgets are produced at that point? (please put your answer in numerical values with no comma or decimal place). If k = 10, at what level of labor input does MPL = 0? Suppose capital inputs were increased to k = 20, at what level of labor input does this average productivity reach maximum? widgets are produced at that point? (please put your answer in numerical values with no comma or decimal place). If k = 20, at what level of labor input does MPL = 0? answer in numerical values with no comma or decimal place). Does the widget production function exhibit constant, increasing, or decreasing returns to scale?…
Suppose you run a factory whose short-run production function is given by f (L) = 180L² – 3L³. (a) Find mathematical expressions for the total product of labor, the average product of labor and the marginal product of labor. (b) On two separate axes, graph T PL, APL, and MPt. The diagrams do not need to be scale, but be sure they are internally consistent. In other words, make sure that all relevant relationships between the three lines are correct. If you have trouble figuring out what the graph looks like, feel free to use a graphing calculator or an online graphing tool to find the basic shape. Find the quantity of labor associated with each of the following points and label it on your diagram: (i) the maximum value of TPL, (ii) the maximum value of APL, (ii) the maximum value of M PL. (c) For what values of L does the production function exhibit each of the following: i. increasing marginal labor productivity ii. diminishing marginal labor productivity iii. negative marginal labor…
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Suppose that a rock star gives concerts. The production function of the concert is the following: Q(C,A,G) = (C – 10)'/4A/4G/4 where C represents hourly contribution of guitarist Chris; A represents hourly contribution of guitarist Ataman and G represents hourly contribution of guitarist George. a) If Chris has 26 units of hours, is there increasing returns to scale in production of concerts? b) Assume George has fixed amount of hours, G=16, and hourly wage of G is 5. Denote the wage of Chris= r and the hourly wage of Ataman =w. Derive Rock star's demand for inputs-C and A, respectively-as a function of output (Q). c) Assume that George has fixed amount of hours G=16 and hourly wage of G is 5. Additionally, you are given that the wage of C = r=100 and the unit wage of Ataman=w=100. Show that Rock star's short run cost function is given by TC(Q) = 1000 +50Q²-
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