Suppose the demand curve for a product is given by Qd 300

Suppose the demand curve for a product is given by Qd = 300 - 2P + 4I, where I is average income measured in thousands of dollars. The supply curve is Qs = 3P - 50.

a. If I=25, find the market-clearing price and quantity for the product.

b. Find the own price elasticity of demand at the equilibrium price and quantity.

c. What is the interpretation of the value of the coefficient of elasticity computed in part \"b\"?

d. Find the income elasticity of demand at the equilibrium price and quantity.

e. What is the interpretation of the value of income elasticity computed in part \"d\"?

f. Find the price elasticity of supply at the equilibrium price and quantity.

g. What is the interpretation of the value of price elasticity computed in part \"f\"?

Solution

Suppose the demand curve for a product is given by Qd = 300 - 2P + 4I, where I is average income measured in thousands of dollars. The supply curve is Qs = 3P - 50.

a. If I=25, find the market-clearing price and quantity for the product.

Qd = 300-2P +4(25) = 400-2P

Qs = 3P-50

Equilibrium is established where Qd = Qs

400-2P = 3P-50

5P = 450

P = 90

Q = 400-2(90) = 220 units

b. Find the own price elasticity of demand at the equilibrium price and quantity.

EDp = P/Q *cofficient fo demand curve

90/220*-2 = 0.818

c. What is the interpretation of the value of the coefficient of elasticity computed in part \"b\"?

Price elasticity of demand is inelastic. It implies with fall in price, total revenue wll fall and with rise in price, total revenue will rise. It means that percentage change in quantity demand is prercentage change in demand.

d. Find the income elasticity of demand at the equilibrium price and quantity.

At equilibrium price Qd = 300-2(90) +4I

120+4I

EDi = P/Q*cofficent of demand curve

90/220*4 = 1.63

e. What is the interpretation of the value of income elasticity computed in part \"d\"?

It means this good is income elastic. It implies with increase in income, its demand will increase more than proportionately.

f. Find the price elasticity of supply at the equilibrium price and quantity.

Qs = 3P-50

ESp = P/Q*cofficent of supply curve

90/220*3 = 1.22

g. What is the interpretation of the value of price elasticity computed in part \"f\"?

Price elasticity of supply is more than one. It means when there is change in price, quantity supply changes more than proportionately.