Question

Karl’s income elasticity of demand for peanut butter is 0.20 while his price elasticity of demand for peanut butter is -1.20.    Karl’s income is $20,000 per year and the price of peanut butter is currently $4.00.    Karl currently spends $2,000 per year on peanut butter   Pea butter is taxed which increases its price by 5%.

a. Calculate what happens to Karl’s purchases of peanut butter.

b. Will Karl end up spending on peanut butter after the price increase? Explain

c. If Karl’s income increased by $100 (5% of 2,000) would he consume the same amount of peanut butter as he did before the price increase? Explain.

Answer 1

Given that the income elasticity of demand for peanut butter is 0.20. Similarly the price elasticity of demand for peanut butter is -1.20. Currently the income is $20,000 per year and the price of peanut butter is $4.00. Spending on butter is $2,000 per year. Hence currently the consumption is Qd = 2000/4 = 500 units.

a) There is a tax on Peanut butter so its price is increased by 5%. Then its price becomes 4.00 + 5%*4.00 = $4.20. With the price elasticity being -1.20, the change in quantity demanded is

ed = % change in Qd/% change in P

-1.2 = % change in Qd/5%

the new quantity demanded is 6% less and it is now 500 - 6% of 500 = 470 units. Spending on peanut butter is now 470 x 4.2 = $1974. Hence spending on butter falls.

b) As we see the spending on peanut butter after the price increase, has decreasd from $2000 to $1974.

c. Now that income is increased by $100 which is 5% of 2,000, his income elasticity is 0.20. His consumption will now be

em = % change in Qd/% change in M

0.20 = % change in Qd/5%

Consumption increases by 1%. Hence he would now consume more peanut butter because his income elasticity is positive. Peanut butter is a normal good for Karl and so when his income increases he consumes more of it.