Question

You are the manager of a company that sells iPhone cases. The costs of producing the cases are given by C = 200 + 20Q (or the fixed costs are $200 and the variable costs are $20 per case). The demand for the cases is given by QD = 180 – 5P.

a) What is the firm’s optimal quantity and price?

b) What is the firm’s profit at the optimal quantity and price?

c) If the fixed costs decrease from $200 to $100, what is the new optimal price and quantity? What is the firm’s new profit?

d) If the variable costs increase from $20/unit to $24/unit, what is the new optimal price and quantity? What is the firm’s new profit?

Answer 1

Answer : Firm optimal price and quantity has been determining as follows :

C=200+20Q

MC=20

Q=180-5P

5P=180-Q

P= 36-Q/5

PQ=36Q-Q ²/5

MR= 36-2Q/5

Profit Maximisation level

MR=MC

36-2Q/5= 20

36-20= 2Q/5

16= 2Q/5

2Q=80

Q=40units

P= 36-Q/5= 36-8=$28

b : Firm profit =TR-TC

Firm profit = 36Q-Q ²/5 - 200-20Q = 16Q-Q ²/5 -200

16(40)-((40)²/5)-200= $120

c : Fixed cost decrease $200 to $100 than effect is

TR = 36Q -Q^{​​​​​ 2} /5

MR=36-2Q/5

C= 100+20Q

MC= 20

Therefore optiumal price is $28 and optiumal Quantity is 40 units.

Firms new profit=TR-TC= 16Q-Q ²/5 -100= $220

d : Variable cost increase it means

C= 200+24Q

MC=24

MR= 36-2Q/5

MR=MC

36-2Q/5=24

36-24=2Q/5

12= 2Q/5

Q= 30 units

P= 36-Q/5 = 36-(30/5)= $30

Profit = 36Q-Q ²/5 - 200-24Q

Profit = 12Q-Q²/5-200= $360-$380=($20)

Loss of $20 when variable cost increases from $20 to $24 and fixed cost remains the same.