1. In the theory of consumer behavior, certain axioms about the nature of preferences imply that indifference curves cannot cross. Which axioms imply this? Explain your answer using a diagram and using words.

2. A consumer decides not to buy a VCR when her income is $20,000. However, when her income rises to $30,000, she decides to buy one. In a single diagram, draw the budget lines and indifference curves to illustrate this situation (assume the VCR costs $300 in both time periods). Be sure to label your diagram completely.

3. An individual consumes products X and Y and spends $25 per time period. The prices of the two goods are $3 per unit for X and $2 per unit for Y. The consumer in this case has a utility function expressed as:

U(X,Y) = 0.5XY MUX = 0.5Y MUY = 0.5X.

a. Express the budget equation mathematically.

b. Determine the values of X and Y that will maximize utility in the consumption of X and Y.

c. Determine the total utility that will be generated per unit of time for this individual.

4. 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.

5. 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.

6. 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?

7. 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?

Question

1. In the theory of consumer behavior, certain axioms about the nature of preferences imply that indifference curves cannot cross. Which axioms imply this? Explain your answer using a diagram and using words.

2. A consumer decides not to buy a VCR when her income is $20,000. However, when her income rises to $30,000, she decides to buy one. In a single diagram, draw the budget lines and indifference curves to illustrate this situation (assume the VCR costs $300 in both time periods). Be sure to label your diagram completely.

3. An individual consumes products X and Y and spends $25 per time period. The prices of the two goods are $3 per unit for X and $2 per unit for Y. The consumer in this case has a utility function expressed as:

U(X,Y) = 0.5XY MUX = 0.5Y MUY = 0.5X.

a. Express the budget equation mathematically.

b. Determine the values of X and Y that will maximize utility in the consumption of X and Y.

c. Determine the total utility that will be generated per unit of time for this individual.

4. 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.

5. 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.

6. 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?

7. 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?

Accepted Answer

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