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# What are the price and output if the oligopolistic firms set the price equal to the marginal cost?

The can industry is composed of two firms. Suppose that the demand curve for cans is
P=100-Q
Where P is the price (in cents) of a can and Q is the quantity demanded (in millions per month) of cans. Suppose that the total cost function of each firm is
TC=2+15q
Where TC is the total cost (in tens of thousands of dollars) per month and q is the quantity demanded (in millions) per month by the firm.
a.What are the price and output if the firms set the price equal to the marginal cost?
b.What are the profit maximizing price and output if the firms collude and act like a monopolist?
c.Do the firms make a higher combined profit if they collude than if they set price equal t marginal cost? If so, how much higher is their combined profit?

#### Solution Preview

Solution:

a. What are the price and output if the firm set price equal to marginal cost?
TC = 2+15q
Marginal Cost = MC=d(TC)/dq=15
Marginal cost per piece=15*10000/1000000=15 cents
It is given that price = MC=15
Both firms have equal total cost function, So, Both will have equal marginal cost, i.e. same price in the given situation.
Let us calculate total demand, at P=15
P=100- Q
15=100-Q
Q=85

Total ...

#### Solution Summary

Solution describes the steps for determining output of oligipoly firms if they set price equal to marginal cost. It also calculates the changes in profits if firms collude and act as a monopolist.

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