Question

1. Suppose the income elasticity of demand for food is 0.5, and the price elasticity of demand is -1.0. Suppose also that Felicia spends $10,000 a year on food, and that the price of food is $2 and her income is $25,000.

   1. If a $2 sales tax on food were to cause the price of food to double, what would happen to her consumption of food?

   2. Suppose that she is given a tax rebate of $5,000 to ease the effect of the tax. What would her consumption of food be now?

Answer 1

Given, Income elasticity = 0.5, price elasticity = - 1

Felicia spends $ 10,000

Price = $ 2, Income = $ 25,000

Units consumed = $ 10,000 / $ 2 = 5,000 units

When a sales tax of $ 2 is imposed then, the price would be $ 4

The mid point (arc) elasticity can be determined using the following formula

Before the sales tax she was buying 5,000 units of food now she is buying 2,500 units. She used to spend = $ 2 × 5,000 = $ 10,000.

Now after the sales tax her expenses on food = $ 4× 2,500

= $ 10,000

That is after the price change her expenses are same on food but consumes only 2,500 units.

B. Tax rebate of $ 5,000 means an increase in income by $ 5,000. Here Quantity 1 is 2,500 units. Since, we have to determine the impact after sales tax and tax rebate.

We can determine the impact through income elasticity

After the tax rebate she will consume 2,738 units. That's after tax rebate she consumes 2738 units of food.

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