Question

You operate a small microbrewery in Germany. The demand curve for cases of your beer is p=50-.002Q. Your marginal cost for producing beer is 10 euros per case. Currently you are charging all customers the same price for a case of your beer.

1. What are the optimal price , quantity , and profits under this pricing policy?

2. Calculate the surplus that goes to consumers.

Answer 1

1.

p=50-0.002Q

Total Revenue=TR=p*Q=50Q-0.002Q^2

Marginal Revenue=MR=dTR/dQ=50-0.004Q

Set MR=MC for profit maximization

50-0.004Q=10

0.004Q=40

Q=40/0.004=10000 (optimal quantity)

p=50-0.002*Q=50-0.002*10000=30 euro (optimal price)

Profit=TR-TC=p*Q-MC*Q=(P-MC)*Q=(30-10)*10000=200000 euro

2.

For finding the CS let us find the price at which quantity demanded is zero

i.e.

p=50-0.002*0=50

CS is the area under demand curve above market price

CS=1/2*(50-30)*(10000-0)=100000 euros