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Decision Making

Please refer attached file for graphs.

With reference to the isocost curve and isoquant below, and the knowledge that labor costs $150 per unit, answer the following questions:

a. What is the price of capital?
b. What is the equation of the isocost curve?
c. What is the slope of the isocost curve?
d. If the marginal product of capital is 50 at the optimal combination of labor and capital (Point B), then what is the marginal product of labor and why? (Hint: Use mathematical conditions for optimal combination).
e.At Point A, which is greater, MPL/w or the MPK/r?
f. At Point C, the same output can be produced more cheaply by substituting _________ for __________.

2. You are the production manager of a price-taking firm. Market price is currently $25 and the chart below depicts your marginal revenue, marginal cost, average total cost and average variable cost curves.

a. Should you produce or shut down when price is $25? Why?
b. What is your profit maximizing output?
c. What is your total revenue at the optimal output?
d. What is your total fixed cost?
e. What is your total variable cost at the optimal output?
f. What is your total profit at the optimal output?
g. Demonstrate how the output associated with the maximum profit rate is not the profit maximizing output
h. Assume the market price falls to $10. Should you produce or shut down at $10? Why?
i. If you produce, how much should you produce?
j. If you produce, what is your total profit?

Attachments

Solution Preview

Please refer attached file for graphs.

1. a. What is the price of capital?

Labor cost=w=$150
Capital cost=r=?
Optimal Point is B at which
Number of capital units=K=45
Number of labor units=L=30
Total Cost at B=45r+30w=45r+30*150=45r+4500
Total cost at labor axis intercept=60*150=$9000
We know total cost along isocost curve is same. So,
45r+4500=9000
45r=4500
r=100
So, Capital cost=r=$100 per unit

b. What is the equation of the isocost curve?

We have two points on isocost curve given by
(L1, K1)= (0,90)
(Ll2, K2)=(30,45)
Slope of isocost line=m=(K2-K1)/(L2-L1)=(45-90)/(30-0)=-45/30=-1.5
Equation of isocost line=K-K1=M*(L-L1)
i.e. K-90=-1.5*(L-0)
K-90=-1.5L
K+1.5L=90

c. What is the slope of the isocost curve?

As calculated in part b, slope of isocost curve is -1.5

d. If the marginal product of capital is 50 at the optimal combination of labor and capital (Point B), then what is the marginal product of labor and why? (Hint: Use mathematical conditions for optimal combination).

Given Marginal product of capital=MPK=50
Marginal product of labor=MPL=?
Labor cost=w=$150
Capital cost=r=$100
We know at optimal point ...

Solution Summary

There are two problems. Solution to first problem determines slope and equation of isocost curve. Solution to second problem demonstrates the methodology to find optimal output level in the given cases.

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