Question

suppose the demand curve for product Y is given by P=150+2i-(Q/2), where i is income measured in thousands of dollars, P is price of product Y in $, Q is quantity of product Y. The supply curve is Q=3P+50, if i=25.

1.What is the price elasticity of demand for product Y at the equilibrium?

2.What is the income elasticity of demand for product Y?

Answer 1

Ans.) We need to find the equilibrium quantity and price first:

As i = 25 , then

P = 150 + 2i - (Q/2)

P = 150 + 2(25) - Q/2

P = 200 - Q/2 ..............eq(1)

The inverse supply is as follows:

- 3P = 50 - Q

P = Q/3 - 50/3

At equlibrium, price is same. So,

200 - Q/2 = Q/3 - 50/3

200 + 50/3 = Q/3 + Q/2

(600+50)/3 = (2Q + 3Q)/6

2(600+50) = (2Q + 3Q)

1200 + 100 = 5Q

1300 = 5Q

Q = 1300/5

Q = 260

P = 200 - Q/2

P = 200 - 260/2

P = 200 - 130

P = 70

Equilibrium price = $70

Equilibrium quantity = 260 units

Price elasticity of demand formula is as follows:

E_d  = (change in quantity/change in price)*(Price/Quantity)

Using eq(1) to find the inverse demand function gives,

Q = 400 - 2P

As the quantity changes by 2 units if price changes (coefficient of 'P'). Thus,

E_d = (-2)(70/260)

E_d = price elasticity =   - 0.54

Ans 2.) Re- writing the demand function in terms of price and income gives,

Q = 300 + 4i - 2P

As we can see that quantity demanded changes by 4 ynits when the price changes by one unit. So , income elasticity of demand is as follows:

I_d = (change in quantity/change in income)*(income/quantity)

I_d = 4(25/260)

I_d = 0.39

Income elasticity of demand = 0.39