Problem set 4: basic theory of the firm
J. Wahl – Microeconomic Principles – Winter 2009
1. Please explain the following statement: "The demand curve for the product of a
perfectly competitive firm is horizontal, while the demand curve for the industry's
product is downward sloping."
2. Suppose you are a competitive jeans manufacturer with the following
information:
You are leasing a warehouse filled with cutting boards and sewing machines for $500
a week. This sum must be paid whether you produce anything or not.
The total jeans one worker could produce in a week is 40 pairs, the total two could
produce is 100 pairs, three could produce 150, four 188, five 221, six 240, seven 250,
and eight 255.
In order to keep the International Ladies' Garment Union happy, you must pay each
of your employees $250 a week.
The ILGU has a monopoly over the denim market. Even though the material for a
pair of blue jeans only costs the ILGU 50 cents, their contract with you states that
they will supply you with all the material you need, but you must pay them $50 for
each worker you hire. That is, the total cost associated with each employee is the sum
of the wages paid to the employee ($250) and the material money you pay the union
($50).
a. Please state the number of jeans you would produce, the number of workers you
would hire, and your profits if the market price is $30 for a pair of jeans.
b. Please state the same information if the market price is $7.
c. Please state the same information if the market price is $5.
d. This problem illustrates the decisions a competitive producer would make under
different assumptions about the relationship of market price to costs. Please summarize
and explain the decision process a competitive producer goes through when deciding
what output to produce.
3. Suppose the total cost function for a competitive firm producing dog collars in the
long-run is TC=1/6 q3 - 5q2 + 65q. Then MC=1/2 q2 - 10q + 65. AC simply equals TC/q.
Suppose the total industry demand for dog collars is given by Q=15110 - 4p. Please use
this information to determine the quantity of collars each competitive firm in the industry
will produce in the long run, the equilibrium industry price, and the number of firms in
the industry.
4. Suppose you manage a firm operating in a competitive market. Your cost of
production is C = 100+q2 where q is the level of output and C is total cost. (The cost
equation tells us that fixed costs are 100 and marginal cost is 2q.) If the price of your
product is $60 per unit, how many units should you produce? What is your profit? At
what minimum price will your firm produce a positive output?
5. T/F and explain. We would never expect to see a firm operating at a quantity
where there are decreasing returns to scale in production in the long run.
