Question

# 1) Suppose a firm faces the following demand curve: q(p) = 100,000– 7,250p and it costs...

1) Suppose a firm faces the following demand curve: q(p) = 100,000– 7,250p and it costs them \$5 to make each unit of their product and their fixed costs are \$15,000.

a. What price will the firm charge? Round your answer to the nearest 2 decimal places.

b. At that price found in #25 what quantity will they produce? Round your answer to

the nearest whole unit.

c. What are the break-even prices? Round your answers to the nearest two decimal

places.

d. What is the highest profit they can make? Round your answer to the nearest dollar.

Total cost of production =5q+15000 = 5*(100000-7250p)+15000

a) Profit, W = Total revenue - total cost

W = pq- (5*(100000-7250p)+15000) = p*(100,000– 7,250p) - (5*(100000-7250p)+15000)

To maximize W

dW/dp = 0

dW/dp = 100,000– 14500p + 36250 = 0

14500p =63750

p= 9.40

Price = \$9.4

b) Quantity = 100000-7250*9.4 = 31850

c) Let breakeven price = p

Total revenue = total cost

p*(100,000– 7,250p) = 5*(100000-7250p)+15000

7250p^2 -136250p +515000 = 0

p =5.24 and 13.55

Break even prices are 5.24 and 13.55.

d) highest profit = profit at price 9.4

Profit = 9.4*31850-31850*5-15000 =\$125140

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