Download List 9. The production function and the marginal product

List 9.
The production function and the marginal product
Task 1.
A commercial fisherman notices the following relationship between hours spent fishing and the
quantity of fish caught:
Hours
Quantity of fish (in
pounds)
0
0
1
10
2
18
3
24
4
28
5
30
a) What is the marginal product of each hour spent fishing?
b) Use these data to graph the fisherman’s production function. Explain its shape.
c) The fisherman has a fixed cost of $10 (his pole). The opportunity cost of his time is $5 per
hour. Graph the fisherman’s total-cost curve. Explain its shape.
Task 2.
Nimbus, Inc., makes brooms and then sells them door-to-door. Here is the relationship between the
number of workers and Nimbus’s output in a given day:
a) Fill in the column of marginal products. What pattern do you see? How might you explain it?
b) A worker costs $100 a day, and the firm has fixed costs of $200. Use this information to fill in
the column for total cost.
c) Fill in the column for average total cost. (Recall that ATC = TC/Q.) What pattern do you see?
d) Now fill in the column for marginal cost. (Recall that MC = dTC/dQ.) What pattern do you
see?
e) Compare the column for marginal product and the column for marginal cost. Explain the
relationship.
f) Compare the column for average total cost and the column for marginal cost. Explain the
relationship.
Microeconomics
Dr Anna Kowalska-Pyzalska
List 9.
The production function and the marginal product
Task 3.
In the short-run the firm cannot change the financial capital, but can adjust the number of workers.
The table below presents how the quantity produces is changing in response to the increasing
number of workers.
a) Calculate the marginal and average products.
b) Present both curves on the graph
c) Starting of which level of production the property of the diminishing marginal products
begins?
d) At which level of production both curves intersect?
Labor (numer of workers
per week)
Production (units per
week)
0
1
2
3
4
5
6
0
35
80
122
156
177
180
Marginal product
Average product
Task 4.
The production function is described by the equation: Q=L*K, where Q is the production, K – financial
capital and L - labor. The wage is equal to 5 and price of the unit of capital is equal to 10.
a) Calculate the marginal product of labor and of capital.
b) Draw the isoquant, which enables production of 10 units per week
c) What is the marginal substitution rate (MSR) between inputs of labor and capital, if K=2 units
and L = 5 units.
d) What should the labor (L) and capital (K) inputs be, to maximize the production, if the total
cost = 100?
Task 5.
The firm engages 50 units of capital and employs 10 workers. The price of the capital is 100/unit and
the wage is 50/worker. Marginal product of labor is equal to 40 and marginal product of capital is
equal to 60.
a) Does the firm minimizes its inputs?
b) If not, what should be changed to find the optimal level of labor and capital for this firm?
c) What would be the answer of the point a) if the price of capital increases to 150/unit and the
wage to 100/worker?
Task 6.
The only variable input a janitorial service firm uses to clean offices is workers who are paid a wage,
w, of $8 an hour. Each worker can clean 4 offices in an hour. What are the variable cost, the average
variable cost, and the marginal cost of cleaning one more office?
Task 7.
The U.S. government subsidizes various crops. To keep its costs down, it prohibits farmers from
increasing the amount of land used to grow those crops. What is the effect of this restriction on the
combination of factors of production that farmers use and on their cost of producing?
Microeconomics
Dr Anna Kowalska-Pyzalska