CHAPTER 4

7. Suppose the marginal rate of substitution is constant at 6 for all possible consumption

bundles. Next suppose that the price of good 1 decrease, and the ratio P1/P2 is greater

than 6.Show that the income and substitution effects from this price change are both

zero.

8. The following data pertain to products A and B, both of which are purchased by

Madame X.Initially, the prices of the products and quantities consumed are:

PA = $10, QA = 3, PB = $10, QB = 7.

Madame X has $100 to spend per time period.After a reduction in price of B, the prices

and quantities consumed are:

PA = $10, QA = 2.5, PB = $5, QB = 15.

Assume that Madame X maximizes utility under both price conditions above.Also,

note that if after the price reduction enough income were taken away from Madame X

to put her back on the original indifference curve, she would consume this combination

of A and B:

QA = 1.5, QB = 9

a. Determine the change in consumption rate of good B due to (1) the substitution

effect and (2) the income effect.

b. Determine if product B is a normal, inferior, or Giffen good.Explain.

9. Joe's Pig Palace sells barbecue plates for $4.50 each, and serves an average of 525

customers per week.During a recent promotion, Joe cut his price to $3.50 and observed

an increase in sales to 600 plates per week.

a. Calculate Joe's arc price elasticity of demand.

b. Joe is considering permanently lowering his price to $4.00 to increase revenue.

How many plates should Joe expect to sell at the new price?Does the move make

sense in the light of Joe's desire to increase revenue?

10. Sally Henin has a price elasticity of demand for gasoline of -0.8.Her income elasticity

for gasoline is 0.5.Sally's current income is $40,000 per year.Sally currently spends

$800 per year on gasoline.The price of gasoline is currently $1.00 per gallon.

a. A contemplated excise tax on gasoline will cause the price of gasoline to rise to

$1.40.What impact will the tax have on Sally's consumption of gasoline?

b. Since the purpose of the tax is only to discourage gasoline consumption, Congress

is considering a $200 income tax rebate to lessen the burden of the gasoline tax.

What impact will the rebates have on Sally's consumption of gasoline?

c. Assume that both the tax and rebate are implemented.Will Sally be worse off or

better off?