Water is produced and sold by the government. Demand for water is represented by the linear function Q=50-2P. The total cost function for water production is also a linear function: TC(Q) = 100 + 10Q. a. Show and explain how much the government should charge per unit of water to reach efficient allocation? b. Show and explain how much the government should charge if it wishes to maximize profit from the sale of water? What are profits? c. What is the value of the efficiency loss that results from charging the profit maximizing price in part “b” rather than the price determined in part “a”.

In order for Government to reach efficient allocation it needs to charge where MC and demand curve intersect. This point considered as the socially efficient quantity of output and this is where total surplus is maximized. In our graph this is shown with Q2.

TC=100+10Q

MC=10 which is derivative of TC.

MC=Demand

We need to find demand as function of Q instead of P as given. Therefore we solve for Q.

P=25-0.5Q

P=MC

25-0.5Q=10

Q=30 and P=10

In order to maximize the profit of selling water the government should produce where MR=MC

TR=P*Q

TR=(25-0.5Q)*Q

TR=25Q-0.5Q^2

MR=25-Q

MR=MC

25-Q=10

Q=15

P=25-0.5Q

P=25-7.5=17.5

PROFIT=P*Q-TC

PROFIT=17.5*15-100 - 10(15)=12.5

Value of efficiency loss=((17.5-10)*15)/2=56.25