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Homework 5
Econ 201
Instructions
All problems are worth 25 points. Partial credit will only be awarded if you show your work.
1. Graph the short run total product, marginal product, and average product curves for each of the following production function if K is fixed at K = 10.
Q = f (K, L) = 5K + L
Q = f (K, L) = (KL)
1
2
(a) Do the two production functions in Problem 1 obey the law of diminishing returns?
1
(1)
(2)
2. Explain in words why an employer would never want to stop increasing the quantity of labor employed when the marginal product is above the average product of labor.
2
3. The Philadelphia Police Department must decide how to allocate police officers between West Philadelphia and Center City. Police can only be deployed in groups of 100.
(a) Measured in arrests per hour, fill in the average product, total product, and marginal product in each of these two areas in the table below. Note that the interpretation of the figures in the table below is per 100 officers as follows: when 100 police officers are deployed in West Philly they get
60 arrests per hour. Similarly, the first 100 police officers in Center City get 75 arrests per hour.
Number of Police
0
100
200
300
400
500
West Philly
AP TP MP
0
0
60
120
180
240
300
Center City
AP TP MP
0
0
75
65
35
25
5
(b) Currently the police department allocates 300 police officers to Center City and 200 to West
Philadelphia. If police can be redeployed only in groups of 100, how, if at all, should the police department reallocate its officers to achieve the maximum number of arrests per hour?
3
4. Suppose that the economy improves and the crime rate in West Philadelphia drops, so that the marginal product and average product of a group of 100 police officers is now 55 arrests per hour for any number of police officers. What is the optimal allocation of 500 police officers between the two areas now?
4
Econ 201
Instructions
All problems are worth 25 points. Partial credit will only be awarded if you show your work.
1. Graph the short run total product, marginal product, and average product curves for each of the following production function if K is fixed at K = 10.
Q = f (K, L) = 5K + L
Q = f (K, L) = (KL)
1
2
(a) Do the two production functions in Problem 1 obey the law of diminishing returns?
1
(1)
(2)
2. Explain in words why an employer would never want to stop increasing the quantity of labor employed when the marginal product is above the average product of labor.
2
3. The Philadelphia Police Department must decide how to allocate police officers between West Philadelphia and Center City. Police can only be deployed in groups of 100.
(a) Measured in arrests per hour, fill in the average product, total product, and marginal product in each of these two areas in the table below. Note that the interpretation of the figures in the table below is per 100 officers as follows: when 100 police officers are deployed in West Philly they get
60 arrests per hour. Similarly, the first 100 police officers in Center City get 75 arrests per hour.
Number of Police
0
100
200
300
400
500
West Philly
AP TP MP
0
0
60
120
180
240
300
Center City
AP TP MP
0
0
75
65
35
25
5
(b) Currently the police department allocates 300 police officers to Center City and 200 to West
Philadelphia. If police can be redeployed only in groups of 100, how, if at all, should the police department reallocate its officers to achieve the maximum number of arrests per hour?
3
4. Suppose that the economy improves and the crime rate in West Philadelphia drops, so that the marginal product and average product of a group of 100 police officers is now 55 arrests per hour for any number of police officers. What is the optimal allocation of 500 police officers between the two areas now?
4