Question

Questions 1 and 2 rely on the following information: Firm A operates in a perfectly competitiveindustry with market price of output, P = $48/unit. Firm A’s total cost given by

TC(q)= q³ + 100

1.What is Firm A’s profit maximizing output level?

2.What price will Firm A charge when maximizing its profit?

3.How much profit is Firm A currently earning given t his price and output level (from #1)?

Answer 1

The equilibrium of perfect competition is achieved where P= MC

we are given the price and the TC function TC(q)= q³+ 100

finding first order condition of the TC we get

MC= 3q²

equating P= MC we get

3q² = 48

q= 16^1/2= 4

so profit maximising output level is 4 units

2) The price firm will charge would be the same as given in the question ie $48 per unit

3) profit = revenue - cost

revenue is product of price of one unit * units purchased

so p*q= 48q = 48*4 = 192

cost is q3 + 100= 64+100=164 where q= 4

so profit = 192-164 = $28 which the profit