Question

The following relations describe the supply and demand for posters.

Qd = 65,000 – 10,000 P
Qs = -35,000 + 15,000P

Where Q is the quantity and P is the price of a poster, in dollars.
a. Complete the following table.

Price Qs Qd Surplus or Shortage
$6.00
5.00
4.00
3.00
2.00
1.00

b. What is the equilibrium price?


Chapter 4 Page 108 Problem 2

The demand function for a cola-type soft drink in general is Q = 20-2P, where Q stands for quantity and P stands for price.

1. Calculate point elasticities at prices of 5 and 9. Is the demand curve elastic or inelastic at these points?
2. Calculate arc elasticity at the interval between P = 5 and P = 6.
3. At which price would a change in price and quantity result in approximately no change in total revenue? Why?


a. Is just a metter of plugging in numbers.
When P = $6, Qd (demand) = 5000 and Qs = 55,000, for a surplus of 50,000.
When P=$4, 4, Qd = 25,000 and Qs = 25,000
etc
b. Clearly the equilibrium price is $4, since that is where Qs=Qd

For problem 2, review the definitions of point and arc elasticites and compute the approprate values.

Revenue is
R = P*Q = 20P - 2P^2.
dR/dP = 0 when 20 - 4P = 0
P = $5 is the price at which small price changes do not affect revenue

Answer 1

The Equilibrium price is $4