Question

1. Show a consumer’s budget constraint and indifference curves for soda drinks and slices of pizza. Show the optimal consumption choice. If the price of soda drinks is $1.50 per can and the price of a slice of pizza is $2 per slice, what is the marginal rate of substitution at the optimum?

2. Suppose the income elasticity of demand for food is 0.5 and the price elasticity of demand is −0.25. Suppose also that Mia spends $10,000 a year on food, the price of food is $2, and that her income is $35,000. (10 pts)

a. If a sales tax on food caused the price of food to increase to $2.50, what would happen to her consumption of food?

(Hint: Because 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 Mia gets a tax rebate of $500 to ease the effect of the sales tax. What would her consumption of food be now?

3. You run a small business and would like to predict what will happen to the quantity demanded for your product if you raise your price. While you do not know the exact demand curve for your product, you do know that in the first year you charged $20 and sold 10,000 units and that in the second year you charged $24 and sold 9,000 units.

If you plan to raise your price by 20%, what would be a reasonable estimate of what will happen to quantity demanded in percentage terms? If you raise your price by 20%, will revenue increase or decrease?

4. James has 100 hours per week that he can devote to working or enjoying leisure. His hourly wage is $15, which he spends on consumption goods.

a. Show his budget constraint graphically (on the horizontal axis, plot hours of leisure, and on the vertical axis, plot consumption goods).

b. If he spends all of his time in leisure (100 hours), what is his spending on consumption goods?

c. If he spends all of his time working, what is his spending on consumption goods?

d. His optimum will occur where the highest possible indifference curve is tangent to the budget constraint. Show that on your previous graph.

e. If his wage increases, his budget constraint will shift outward. Will he supply more labor or less labor? Answer this question using a graph.

Answer 1

1. The graph show the budget constraint and IC curves.

The line AB shows the budget constraint of soda and pizza. Where the optimal point of production is where IC2 touches the budget line, as it provides the maximum utility attainable. Whereas, IC3 is unattainable and IC1 is attainable but not not reaching maximum utility.

Marginal rate of substitution(i.e also the slope of the budget constraint) is, = 2.00/1.50 = 1.333