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* 1. Returns to scale in production: Do the following production functions exhibit increasing, constant, or decreasing returns to scale in K and L? (Assume A is some fixed positive number.) (a) Y = K1/211/2 (b) Y = K2/312/3 (c) Y = K1/31/2 (d) Y = K + L (e) Y = K + K1/31/3 (f) Y = K1/3L2/3 + A (g) Y = K1/312/3 - A 2. The "per person" versions of production functions: Write each production function given below in terms of output per person y = Y/L and capital per E

* 1. Returns to scale in production: Do the following production functions exhibit increasing, constant, or decreasing returns to scale in K and L? (Assume A is some fixed positive number.) (a) Y = K1/211/2 (b) Y = K2/312/3 (c) Y = K1/31/2 (d) Y = K + L (e) Y = K + K1/31/3 (f) Y = K1/3L2/3 + A (g) Y = K1/312/3 - A 2. The "per person" versions of production functions: Write each production function given below in terms of output per person y = Y/L and capital per E

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
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
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Question 1 & 2 if possible please. I need the steps to solve these questions. Thanks!
98 Chapter 4 A Model of Production EXERCISES * 1. Returns to scale in production: Do the following production functions exhibit increasing, constant, or decreasing returns to scale in K and L? (Assume A is some fixed positive number.) (a) Y = K ¹/21/2 (b) Y = K2/312/3 (c) Y = K1/3L1/2 (d) Y = K + L (e) Y = K + K1/3L1/3 (f) Y = K1/3L2/3 + A (g) Y= K1/312/3 - A 2. The "per person" versions of production functions: Write each production function given below in terms of output per person y = Y/L and capital per person k = K/L. Show what these "per person" versions look like in a graph with k on the horizontal axis and y on the vertical axis. (Assume A is some fixed positive number.) (a) Y = K1/3L2/3 and Y = K3/4L1/4 (on the same graph) (b) Y = K (c) Y = K + AL (d) Y = K - AL * 3. The Black Death: In the middle of the fourteenth century, an epidemic known as the Black Death killed about a third of Europe's population, about 34 mil- lion people. While this was an enormous tragedy, the macroeconomic con sequences might surprise you: over the next century, wages are estimated to have been higher than before the Black Death. (a) Use the production model to explain why wages might have been highe (b) Can you attach a number to your explanation? In the model, by how much would wages rise if a third of the population died from disease? 4. Solving the production model: Suppose the production function at the co of our model is given by Y = AK 3/4L1/4 (that is, assume the exponents of capital and labor are 3/4 and 1/4 rather than 1/3 and 2/3). (a) Create a new version of Table 4.1 for the new version of the model. Wh are the five equations and five unknowns? (Hint: The hiring rules for capit and labor will change in the obvious way.) (b) Now solve these equations to get the solution to the model. Put you solution in the same form as Table 4.2. (c) What is the solution for the equilibrium level of output per person? 5. The empirical fit of the production model: The table below reports per cap GDP and capital per person in the year 2017 for 10 countries. Your task to fill in the missing columns of the table. (a) Given the values in columns 1 and 2, fill in columns 3 and 4. That compute per capita GDP and capital per person relative to the US val K E 6. r 7. T th th to- of all (a) (b) (c) I
Transcribed Image Text:98 Chapter 4 A Model of Production EXERCISES * 1. Returns to scale in production: Do the following production functions exhibit increasing, constant, or decreasing returns to scale in K and L? (Assume A is some fixed positive number.) (a) Y = K ¹/21/2 (b) Y = K2/312/3 (c) Y = K1/3L1/2 (d) Y = K + L (e) Y = K + K1/3L1/3 (f) Y = K1/3L2/3 + A (g) Y= K1/312/3 - A 2. The "per person" versions of production functions: Write each production function given below in terms of output per person y = Y/L and capital per person k = K/L. Show what these "per person" versions look like in a graph with k on the horizontal axis and y on the vertical axis. (Assume A is some fixed positive number.) (a) Y = K1/3L2/3 and Y = K3/4L1/4 (on the same graph) (b) Y = K (c) Y = K + AL (d) Y = K - AL * 3. The Black Death: In the middle of the fourteenth century, an epidemic known as the Black Death killed about a third of Europe's population, about 34 mil- lion people. While this was an enormous tragedy, the macroeconomic con sequences might surprise you: over the next century, wages are estimated to have been higher than before the Black Death. (a) Use the production model to explain why wages might have been highe (b) Can you attach a number to your explanation? In the model, by how much would wages rise if a third of the population died from disease? 4. Solving the production model: Suppose the production function at the co of our model is given by Y = AK 3/4L1/4 (that is, assume the exponents of capital and labor are 3/4 and 1/4 rather than 1/3 and 2/3). (a) Create a new version of Table 4.1 for the new version of the model. Wh are the five equations and five unknowns? (Hint: The hiring rules for capit and labor will change in the obvious way.) (b) Now solve these equations to get the solution to the model. Put you solution in the same form as Table 4.2. (c) What is the solution for the equilibrium level of output per person? 5. The empirical fit of the production model: The table below reports per cap GDP and capital per person in the year 2017 for 10 countries. Your task to fill in the missing columns of the table. (a) Given the values in columns 1 and 2, fill in columns 3 and 4. That compute per capita GDP and capital per person relative to the US val K E 6. r 7. T th th to- of all (a) (b) (c) I
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