Question

Suppose that the market demand curve for cornflakes cereal is Q = 600 - 40P where Q is the quantity of cornflakes bought in thousands of boxes per week and P is the price per box (in Kwacha).

a) At what price does the demand for cornflakes go to 0? show that the demand for cornflakes is elastic at this price.

b) How much cornflakes is demanded at a price of K0? show that demand is inelastic at this price.

c) What is the price elasticity of demand if a box of cornflakes cost K10

Answer 1

(a)

Demand is given by:

Q = 600 - 40P , where Q is quantity demanded and P = Price

Now we want Q to be equal to 0

=> 0 = 600 - 40P

=> P = 600/40

=> P = 15

Hence, the demand for cornflakes is equal to 0 when Price = K15

Elasticity of demand = (dQ/dP)(P/Q)

Q = 600 - 40P => dQ/dP = -40 and as calculated above P = K15 and Q = 0

=> Elasticity of demand = (dQ/dP)(P/Q) = -40(15/0) = - infinity

Hence, e < -1 => Demand is elastic

(b)

Demand is given by:

Q = 600 - 40P , where Q is quantity demanded and P = Price

Now we want P to be equal to K0

=> Q = 600 - 40*0

=> Q = 600

Hence, the Price of cornflakes is equal to 0 when Quantity = 600

Elasticity of demand = (dQ/dP)(P/Q)

Q = 600 - 40P => dQ/dP = -40 and as calculated above P = K0 and Q = 600

=> Elasticity of demand = (dQ/dP)(P/Q) = -40(0/600) = 0

Hence, e > -1 => Demand is inelastic

(c)

Demand is given by:

Q = 600 - 40P , where Q is quantity demanded and P = Price

Now we want P to be equal to K10

=> Q = 600 - 40*10

=> Q = 200

Elasticity of demand = (dQ/dP)(P/Q)

Q = 600 - 40P => dQ/dP = -40 and as calculated above P = K10 and Q = 200

=> Elasticity of demand = (dQ/dP)(P/Q) = -40(10/200) = -2

The price elasticity of demand if a box of cornflakes cost K10 = -2