Question

1. Suppose there is a perfectly competitive market for latte. The market inverse demand function is given by P = - 0 + 10 Answer the following questions.

Answer 1

P = (-1 / 5) Q + 10

a) Price elasticity of demand = %change in quantity demanded / %change in price

As demand curve is a straight line, its slope would be constant at every price level while elasticity of demand changes at every price level. Thus this statement is false.

b)

• Price when changes from $4 to $5

%change in price = [(5 - 4) / 4] * 100 = 25%

• Price when changes from $5 to $6

%change in price = [(6 - 5) / 5] * 100 = 20%

c)

• Price when changes from $4 to $5

4 = (-1 / 5) Q + 10

Q = 30

5 = (-1 / 5) Q + 10

Q = 25

When price rises from $4 to $5, quantity demanded falls from 30 to 25.

%change in quantity demanded = [(25 - 30) / 30] * 100 = -16.67%

• Price when changes from $5 to $6

5 = (-1 / 5) Q + 10

Q = 25

6 = (-1 / 5) Q + 10

Q = 20

When price rises from $5 to $6, quantity demanded falls from 25 to 20

%change in quantity demanded = [(20 - 25) / 25] * 100 = -20%

d)

• When price rises from $4 to $5, revenue changes from 120 to 125

Price elasticity of demand = -16.67% / 25% = 0.6668 (ignore negative sign due to negative relationship between price and quantity demanded)

Elasticity of demand < 1 is inelastic demand as rise in price does not intend consumers to consume less of the goods which will raise the revenue.

• When price rises from $5 to $6, revenue changes from 125 to 120.

Price elasticity of demand = -20% / 20% = 1 (ignore negative sign due to negative relationship between price and quantity demanded)

Elasticity of demand = 1 is unitary demand.