Question

2. Suppose you are the manager of a watchmaking firm operating in a competitive market. Your cost of production is given by C = 200 + 2q2, where q is the level of output and C is total cost. (The marginal cost of production is 4q; the fixed cost is $200.)

a. If the price of watches is $100, how many watches should you produce to maximize profit?

b. What will the profit level be?

c. At what minimum price will the firm produce a positive output?

Answer 1

Competitive market leads to P=MC for equilibrium

MC=4q and Fixed Cost=$200

Profit=Total Revenue-Total Cost=PQ-C(Q)

Profit=100q-200-2q2

FOC should be equalled to zero

100-4q=0

q=25 hence They should produce 25 watches to earn maximum profit

Answer for b)

Profit=PQ-C(Q)=100*25-(200+2(25^2)=2500-(200+1250)=$1050

Answer for c)

When Profit becomes zero that is the minumum level above which we can guarentee positive profit

Profit=0

TR=TC

Pq=200+2q2

2q2+200-Pq=0

2q2-Pq+200=0

q2-P/2q+100=0

q=P/2+/-sqrt(P^2/4-4(100))/2

q=P/4+(P2/4-400)^(1/2)/2

To be positive output

P^2/4-400>0

P>40

Minimum Price should be 40