Microeconomic Theory
12th Edition
ISBN: 9781337517942
Author: NICHOLSON
Publisher: Cengage
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Chapter 10, Problem 10.5P
a)
To determine
To find:
Allocation of output between factories.
b)
To determine
To know:
Short-run
c)
To determine
To know:
Allocation of widget production between two factories in long run.
d)
To determine
To know:
Allocation of widget production between two factories in long run when diminishing returns sets in.
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Catalina Films produces video shorts using digital editing equipment (K) and editors (L). The firm has the production function Q(K, L)=KxL, where Q is the hours of edited footage. The wage is $25, and the rental rate of capital is $50. The firm wants to produce 3,000 units of output at the lowest possible cost.a) Find the marginal product of each input.b) Determine whether the production function exhibits diminishing marginal product to each input.c) Find the marginal rate of technical substitution(MRTSLK)d) How does MRTSLK change as more L, is used holding output constant.e) Find the least costly combination of labor and capital to produce 3000 units
Catalina Films produces video shorts using digital editing equipment (K) and editors (L). The firm has
the production function Q(K, L)=KxL, where Q is the hours of edited footage. The wage is $25, and
the rental rate of capital is $50. The firm wants to produce 3,000 units of output at the lowest
possible cost.
a) Find the marginal product of each input.
b) Determine whether the production function exhibits diminishing marginal product to each
input.
c) Find the marginal rate of technical substitution (MRTSLK)
d) How does MRTSLK change as more L, is used holding output constant.
e) Find the least costly combination of labour and capital to produce 3000 units.
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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