Suppose a Cobb-Douglas Production function is given byP (L, K) = 10L00.75 0.25where L is units of labor, K is units of capital, and P (L, K) is total units that can be produced withthis labor/capital combination. Suppose each unit of labor costs $700 and each unit of capital costs$2,100. Further suppose a total of $504,000 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 tothe budgetary constraint? Round to the nearest whole number, if necessary.Labor: L=Capital: K-unitsMaximum production:unitsb. What is the maximum number of units of production under the given budgetary conditions?Round to the nearest whole number, if necessary.units

Production function: It is the mathematical representation of the relationship between input…

a. How many units of labor and capital should be "purchased" to maximize production subject to the budgetary constraint? Round to the nearest whole number, if necessary. Labor: L units Capital: K b. What is the maximum number of units of production under the given budgetary conditions? Round to the nearest whole number, if necessary. Maximum production: units units

a. How many units of labor and capital should be "purchased" to maximize production subject to the budgetary constraint? Round to the nearest whole number, if necessary. Labor: L units Capital: K b. What is the maximum number of units of production under the given budgetary conditions? Round to the nearest whole number, if necessary. Maximum production: units units

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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Henry owns a Boba tea shop and produces delicious drinks under the production function q = 5KL where q is the number of servings generated per hour, K is the number of tea pots (capital), and L is the number of employees hired per hour (labor). The average product of labor and the marginal product of labor are both equal to APL = MPL 5K. Does labor exhibit diminishing marginal returns in this case? O No, the marginal product of labor is constant (for a given K). O No, the marginal product of labor is increasing (for a given K). O Yes, if capital also exhibits diminishing marginal returns. O Yes, this is true for all values of K.
se The marginal product of labor can be determined using the total product of labor Production Function curve. 3,500- se Using the equation for the production function, 3,000- 3 2 q= 8LK + 5L2 – 2,500- see the level of output when L= 5 and K= 25 is (Enter a numeric response using 2,000- a real number rounded to two decimal places). 3 1,500- When labor is 5 units and K is 25, the marginal product of labor is 1 1,000 *** When labor increases to 12 units and K is 25, the marginal product of labor is 500 - 12 10 15 Labor Input (L) 15 20 25 DEC 25 tv 20 MacBook Air DII SO F10 F11 F9 F3 F4 * %23 $ & 4 6 8 { } E Y U P D F G н J K > C V N M command option - - ... .- V Product or Output (g) B R
The marginal product of labor can be determined using the total product of labor curve. Production Function Using the equation for the production function, 3,500- q = BLK + 5L2 - 3,000- 2 2,500- the level of output when L= 5 and K = 25 is (Enter a numeric response using a real number rounded to two decimal places). 2 2,000- When labor is 5 units and K is 25, the marginal product of labor is. 1,500- 1 When labor increases to 12 units and K is 25, the marginal product of labor is. 1,000- 500- 12 15 10 0- 15 20 25 Labor Input (L) DEC 20 A の O tv g: 00:39:49 Next MacBook Air DII F2 F3 F4 FS F7 F9 F12 %23 2$ & 2 3 4 5 6 7 8 W E R Y U P { } D G H J K く > ? C V command command option ト Product or Output (q)
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What is the average product of labor, given that the level of labor equals 10, total output equals 1200, and the marginal product of labor equals 200? Suppose the production function is given by Q= K + 2L. What is the average product of capital when 5 units of capital and 2 units of labor are employed?
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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