Question

In: Economics

Suppose the income elasticity of demand for food is 0.5 and the price elasticity of demand...

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!

Solutions

Expert Solution

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.


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