Question

Assume that consumers view tax preparation services as undifferentiated among producers, and that there are hundreds of companies of offering tax preparation in a given market. The current market equilibrium price is S120. Joe Audit's Tax Service has a daily, short-run total cost given by C = 100+4Q^2.
Answer the following questions:
a. How many tax returns should Joe prepare cach day if his goal is to maximize profits?
b. How much will he earn in profit each day?

Answer 1

Answer:

Q = 15

profit at q=15 $800

Explanation:

To maximize their profit it will produce until the marginal cost equalize the marignal revenue.

As the price is 120 each additional unitgenerates 120 dollars of revenue.

Now, we solve for the marginal cost

$C_q = 100+4Q^2\\\frac{dC_q}{dq} =8Q\\\\8Q = 120\\Q = 120 / 8$

Q = 15

Total cost

$C = 100 + 4(15)^2 = 100 + 4(225) = 1,000$

Profit

$120 x 15 units - $1,000 cost = 800