Question

A firm’s revenue is R = 100q – 4q² and cost is C = 100 + 20q. The owner of the firm offers two alternative compensation packages to the manager: 1) 40% share of the company’s profit or 2) 20% of the company’s revenue. Which package will the manager choose?

Answer 1

Case 1 : 40% share of company's profit

Given

R=100q-4q^2

Marginal Revenue=MR=dR/dq=100-8q

C=100+20q

Marginal Cost=MC=dTC/dq=20

Set MR=MC for profit maximization

100-8q=20

8q=80

q=10 (optimal output)

So,

R=100q-4q^2=100*10-4*10^2=600

Total Cost=C=100+20q=100+20*10=300

Profit=R-C=600-300=300

Manager's maximum compensation=40% of profit=300*40%=120

ii) Case 2 : 20% of total revenue

Set MR=0 to maximize revenue

100-8q=0

q=12.50

Total Revenue=R=100q-4q^2=100*12.5-4*12.5^2 =625

Manager's maximum compensation=20% of R=625*20%=125

Maximum package is higher in case of package 2. So, he will choose

2) 20% of the company’s revenue