4 Homework Additional Problem
ECON 010, Fall 2011
Question 1
Consider a market for milk. The demand and supply for milk are as follows:
Demand : P
=
100 2QD
Supply : P
=
20
a) Find the equilibrium quantity, price and revenue generated in this market.
Answer:
We derive the equilibrium quantity by setting supply and demand equal to each other:
100 2Q =
20
Q
=
40
P
=
20
Given the equilibrium price and quantity, we can derive the total revenue generated:
TR
= P Q
=
800
b) Calculate the price of elasticity demand at the equilibrium.
Answer:
P
ED
=
=
P
PM AX P
(20) /(100 20)
= 1/4
c) Suppose that the farmers decide to withhold some of their produced milk in an eort to raise the
price in the market. Find the amount of quantity they will need to withhold such that their total
revenues are maximized.
1
Answer:
P
Total revenue will be maximized at a point where ED = 1. This will occur at a point
where P = 50 and Q = 25. Therefore, the farmers will have to withhold 15 gallons of
milk.
2