Homework6b
Homework 6
Econ 201
1. (20 Points for Each Production Function) 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
(1)
(2)
(a) (10 Points) Do the two production functions in Problem 1 obey the law of diminishing returns?
1
2. (10 Points) 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) (15 Points) 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.
West Philly
Number of Po- AP TP MP lice 0
0
0
–
100
60
200
120
300
180
400
240
500
300
Center City
AP TP MP
0
0
–
75
65
35
25
5
(b) (15 Points) 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?
4. (10 Points) 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?
3
Econ 201
1. (20 Points for Each Production Function) 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
(1)
(2)
(a) (10 Points) Do the two production functions in Problem 1 obey the law of diminishing returns?
1
2. (10 Points) 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) (15 Points) 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.
West Philly
Number of Po- AP TP MP lice 0
0
0
–
100
60
200
120
300
180
400
240
500
300
Center City
AP TP MP
0
0
–
75
65
35
25
5
(b) (15 Points) 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?
4. (10 Points) 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?
3