Consider the following production functions, where q is the quantity produced of the good, K is the quantity of capital used, and L is the quantity of labor used: Production function 1: q (K, L) = KªLB Production function 2: q (K, L) = K² + L 1. Suppose that a = 1 and ẞ= 1. Does Production function 1 have decreasing, constant, or increasing returns to scale? Explain. 2. Suppose that a = 1 and ẞ= 1. Does Production function 2 have decreasing, constant, or increasing returns to scale? Explain. 3. Below is a Total Product table for production function 1 when a = 1 and ẞ = 1. KIL 1 2 3 455 1 12 3 4 5 16 2 24 6 8 10 12 3 36 9 12 15 18 st 48 12 16 20 24 5 5 10 15 20 25 30 6 612 18 24 30 36 Suppose that the level of capital is fixed at 5 units. What is the marginal product of labor (MPL) for each unit of labor employed? Does the MP, vary with number of units of labor used?
Consider the following production functions, where q is the quantity produced of the good, K is the quantity of capital used, and L is the quantity of labor used: Production function 1: q (K, L) = KªLB Production function 2: q (K, L) = K² + L 1. Suppose that a = 1 and ẞ= 1. Does Production function 1 have decreasing, constant, or increasing returns to scale? Explain. 2. Suppose that a = 1 and ẞ= 1. Does Production function 2 have decreasing, constant, or increasing returns to scale? Explain. 3. Below is a Total Product table for production function 1 when a = 1 and ẞ = 1. KIL 1 2 3 455 1 12 3 4 5 16 2 24 6 8 10 12 3 36 9 12 15 18 st 48 12 16 20 24 5 5 10 15 20 25 30 6 612 18 24 30 36 Suppose that the level of capital is fixed at 5 units. What is the marginal product of labor (MPL) for each unit of labor employed? Does the MP, vary with number of units of labor used?
Economics (MindTap Course List)
13th Edition
ISBN:9781337617383
Author:Roger A. Arnold
Publisher:Roger A. Arnold
Chapter17: Economic Growth: Resources, Technology, Ideas And Institutions
Section17.2: A Production Function And Economic Growth
Problem 4ST
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Transcribed Image Text:Consider the following production functions, where q is the quantity produced of the good, K
is the quantity of capital used, and L is the quantity of labor used:
Production function 1: q (K, L) = KªLB
Production function 2: q (K, L) = K² + L
1. Suppose that a = 1 and ẞ= 1. Does Production function 1 have decreasing, constant, or
increasing returns to scale? Explain.
2. Suppose that a = 1 and ẞ= 1. Does Production function 2 have decreasing, constant, or
increasing returns to scale? Explain.
3. Below is a Total Product table for production function 1 when a = 1 and ẞ = 1.
KIL 1 2 3
455
1
12 3
4
5 16
2
24
6 8
10 12
3
36
9 12 15 18
st
48
12 16 20 24
5
5 10 15 20 25 30
6 612 18 24 30 36
Suppose that the level of capital is fixed at 5 units. What is the marginal product of labor (MPL)
for each unit of labor employed? Does the MP, vary with number of units of labor used?
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