Question

Javier runs a shop in which he fixes flat tires; tire repair is a competitive industry. Repairing tires is the only service that he sells, and he receives $12 for each flat tire he repairs. Javier has fixed costs of $150. His variable costs are 0.05Q2, where is the number of flat tires repaired this means that his marginal costs are 0.10. (a) Write down Javier's revenue function. (b) What is Javier's profit function? (c) How many tires should Javier fix to maximize profit? (d) How large are Javier's profits when he chooses the output level you found in (c)?

Answer 1

a) Revenue is PQ. Price is fixed at $12 per unit. Hence revenue function is R(Q) = 12Q

b) Profit = revenue - cost => Profit = 12Q - 150 - 0.05Q^2

c) To maximize profit P = MC must be used. This gives 12 = 0.1Q or Q = 120 tires. Hence Javier should produce / service 120 tires

d) Profit = 12*120 - 150 - 0.05*(120^2)

= $570