Answer to Question #286365 in Microeconomics for rexfer

Question

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

P        Q        S

60      22      14

80      20      16

100    18      18

120    16      20

a. Calculate the price elasticity of demand when the price is $80.

b. Calculate the price elasticity of supply 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?

Answer 1

a) Price elasticity of demand when the price is 80

Price elasticity of demand = %change in quantity demanded divide by %change in quantity supplied.

Change in Demand =

20-22=-2

20+22= 42 divide by 2= 21,

Thus

$\frac{-2}{21}\times100=-9.5238$

Change in Price =

80-60= 20

80+60=140 divide by 2 = 70

Thus:

$\frac{20}{ 70 } \times 100=28.5714$

Price elasticity of demand =

$\frac{ -9.5238}{28.5714}= -0.3333$

Price elasticity of demand = 0.3333

This implies that 1% change in price will lead to 0.3333 percentage change in quantity demanded.

b) The price elasticity of supply when the price is 100

Price elasticity of supply = %change in quantity supplied divide by % change in price

%change in quantity supplied =

Change in cquatity supplied =18-14= 4

18+14 =32 divide by 2= 16

Thus;

$\frac{ 4}{16}\times100= 25$

% change in price =

100-60= 40

100+60= 160 divide by 2 = 80

Thus;

$\frac{40}{80}\times100=50$

Price elasticity of supply =

$\frac{ 25}{ 50}=0.5$

This implies that 1% change in price will lead to 0.5% increase in quantity supplied.

c) Equilibrium price and quantity occurs when the quantity demanded and quantity supplied are the same.

Thus the equilibrium price is 100, and the equilibrium quantity is 18

d) Government sets a price ceiling at 80

A price ceiling at 80 will create shortage in supply since 80 is below the equilibrium price of 100. The shortage created will be equivalent to quantity supplied subtracted from the equilibrium quantity.

Thus; 18-16 = 2 units.