Question

Consider a competitive market for which the quantities demanded and supplied (per year) at various prices are given as follows:

PRICE (DOLLARS)	DEMAND (MILLIONS)	SUPPLY (MILLIONS)
60	22	14
80	20	16
100	18	18
120	16	20

a. Calculate the price elasticity of demand when the price is \(80 and when the price is \)100.

b. Calculate the price elasticity of supply when the price is \(80 and when the price is \)100.

c. What are the equilibrium price and quantity?

d. Suppose the government sets a price ceiling of $80. Will there be a shortage, and if so, how large will it be?

Short answer

a. The price elasticity of demand at $80 will be -0.4 and at $100 will be -0.556.

b. The price elasticity of supply at $80 will be 0.5 and at $100 will be 0.555.

c. The equilibrium price will be $100, and the quantity will be 18 million.

d. This price ceiling will create a shortage of supply by 4 million.

Step-by-step solution

Explanation for part (a)

The price elasticity when the price = $80 would be;

$$\begin{gathered} E_d=\frac{△Q}{△P}\times \frac{P}{Q} \\ △Q=20-22 \\ △P=80-60 \\ =\frac{-2}{20}\times \frac{80}{20} \\ =-0.4 \end{gathered}$$

When price = $100

$$\begin{gathered} E_d=\frac{△Q}{△P}\times \frac{P}{Q} \\ △Q=18-20 \\ △P=100-80 \\ =\frac{-2}{20}\times \frac{100}{18} \\ =-0.556 \end{gathered}$$

Thus, price elasticity at prices $80 and $100 will be -0.4 and -0.556, respectively.

Explanation for part (b)

The price elasticity of supply when price =$80 would be;

$$\begin{gathered} E_s=\frac{△Q}{△P}\times \frac{P}{Q} \\ △Q=16-14 \\ △P=80-60 \\ =\frac{2}{20}\times \frac{80}{16} \\ =0.5 \end{gathered}$$

When price = $100

$$\begin{gathered} E_s=\frac{△Q}{△P}\times \frac{P}{Q} \\ △Q=18-16 \\ △P=100-80 \\ =\frac{2}{20}\times \frac{80}{18} \\ =0.555 \end{gathered}$$

Thus, the price elasticity of supply at prices $80 and $100 would be 0.5 and 0.555, respectively.

Explanation for part (c)

The equilibrium price and quantity are where demand equals the supply. In the table above, we see that both demand and supply are equal at $100. Therefore, equilibrium prices are $100, and the equilibrium quantity is 18 million.

Explanation for part (d)

If the government sets price celling at $80, then the quantity demanded would be 20 million, and the quantity supply would be 16 million (given in the table above). Thus, this will create a shortage of supply of 4 million in the market.