Question

1.) the price elasticity of demand for margarine is -1.3 and the income elasticity of demand for margarine is -0.2.

a. Based on these figures, is the demand for margarine elastic or inelastic? How can you tell?

b. If the price of margarine falls by 5%, by what percentage will the quantity of margarine demanded change? Will it rise or fall?

c. If the price of margarine falls by 5%, by what percentage will the total revenue from sales of margarine (or total consumer spending on margarine) change? Will it rise or fall?

d. If consumer incomes rise by 10%, would the share of consumer income spent on margarine rise, or would it fall? Calculate an estimate of the percentage change in the share of income spent on margarine as a result of a 10% increase in income.

Answer 1

1) The price elasticity of demand for margarine is -1.3 and the income elasticity of demand for margarine is -0.2.

a.

Price elasticity of demand= % change in quantity demand / % change is price

The demand is elastic if value of price elasticity of demand is higher than 1 because it implies that % change in quantity demand is more than the % change is price and inelastic if value of price elasticity of demand is lower than 1 because it implies that % change in quantity demand is less than the % change is price.

Here value of price elasticity of demand for margarine is -1.3 is more than 1 in absolute terms(without considering negative sign) so demand is elastic.

b.

If the price of margarine falls by 5% that is % change is price = - 5%

-1.3= % change in quantity demand / -5%

6.5%= % change in quantity demand

So quantity demand will rise by 6.5%. It is because of negative relationship between price and quantity demand.

c.

Suppose initial price(P1) = 100 and initial quantity(Q1) =  10. Now if the price of margarine falls by 5%. Then

New price(P2)= 100-0.05x100= 100-5= 95

As we calculated in part b, this fall in price cause quantity demand to rise by 6.5%. So

New quantity(Q2)= 10+0.065x10= 10.65

Total revenue= P x Q

Initial Total revenue= P1 X Q1= 100 X 10= 1000

Total revenue after price fall= P2 X Q2= 95 X 10.65= 1011.75

% change in total revenue= (Total revenue after price fall - Initial Total revenue) / Initial Total revenue x 100

% change in total revenue = (1011.75 - 1000)/1000 x 100= 11.75 / 10= 1.175%

Total revenue will rise by 1.175 %.

d.

Income elasticity of demand= % change in demand / % change in income

If Income elasticity is negative it means that due to rise in income, demand for the good decreases and if positive it implies that if income increases, demand also rises.

Here  income elasticity of demand for margarine is -0.2 which is negative so If consumer incomes rise by 10%, it will cause fall in demand for margarine that is share of consumer income spent on margarine fall.

Income elasticity of demand= % change in demand / % change in income

-0.2 = % change in demand / 10%

-2% =% change in demand

Percentage fall in the share of income spent on margarine is 2%.