In: Economics
Suppose the income elasticity of demand for food is 0.5 and the price elasticity of demand is -1.0. Suppose a hypothetical group of people spend $10,000 a year on food, the price of food is $2, and that their total income is $25,000.
a. If a sales tax on food caused the price of food to increase to $2.50, what would happen to their consumption of food?
b. Suppose they will get a tax rebate of $2500 to ease the effect of the sales tax. What would the consumption of food be now?
c. Are they better or worse off when given a rebate equal to the sales tax payments? Explain.
Each part should be answered in 4 sentences thank you!
Income Elasticity of demand = 0.5
It means if income goes up by 1% food demand will go up by 0.5%
Price Elasticity of demand = -1
It means if Price goes up by 1% food demand will go down by 1%
a. Initially quantity of food consumed = 10,000 / 2 = 5,000
The price goes up from 2$ to 2.5$ means price is up by 25% will cause demand to go down by 25% ( as price elasticity is -1 )
The final quantity of food consumed = 5,000 - 0.25 * 5,000 = 3750
tax paid = 3750 * 0.5 = 1,875
total food expenditure = 3750 * 2.5 = 9,375 ( 7500 + 1875 )
b. Tax rebate upto 2,500$
If amount 1,875$ is given back then a unit good would have cost = ( 9,375-1,875 ) / 3750 = 2
This step would have same affect as bringing down price from 2.5$ to 2$ that is bringing price down by 20%
which will increase demand by 20%
final demand = 3750 + 0.2 * 3750 = 4500
( effective price = 2$ because of tax rebate upto 2,500$ )
b. In case when there was no sales tax person consumed 5,000 units at price of 2$
In case when they were given rebate equal to sales tax payment they consumed 4,500 units at price of 2$
they are worse off in later senario.