Question

Suppose the income elasticity of demand for food is 0.5, and the price elasticity of demand is -1.0. Suppose also that a woman spends $10,000 a year on food, and that the price of food is $2, and that her income is $25,000. a. If a $2 sales tax on food were to cause the price of food to double, what would happen to her consumption of food? Hint: Since a large price change is involved, you should assume that the price elasticity measures an arc elasticity, rather than a point elasticity. b. Suppose that she is given a tax rebate of $5000 to ease the effect of the tax. What would her consumption of food be now? c. Is she better or worse off when given a rebate equal to the sales tax payments? Discuss.

Answer 1

$$p_1=2$$

$$p_2=4$$

$$q_1=5000$$

q_2-?

$$E_d^p=\frac{q_2-q_1}{q_2+q_1}\times \frac {p_2+p_1}{p_2-p_1}$$

$$q_2=2500$$

b)

$$p_2'=\frac{(4\times5000-5000)}{5000}=3$$

$$q_2'=3333$$

c)

The introduction of a tax break leads to an improvement in the position of the consumer in the market for these products.