For each of the following situations, decide whether the bundle Lakshani is considering is optimal or not. If it is not optimal, how could Lakshani improve her ‘overall level of utility? That is, determine which good she should spend more on and which good she should spend less on.

a. Lakshani has $200 to spend on sneakers and sweaters. Sneakers cost $50 per pair, and sweaters cost $20 each. She is thinking about buying 2 pairs of sneakers and 5 sweaters. She tells her friend that the additional utility she would get from the second pair of sneakers is the same as the additional utility she would get from the fifth sweater. Lakshani has $5 to spend on pens and pencils. Each pen costs $0.50 and each pencil costs $0.10. She is thinking about buying 6 pens and 20 pencils. The last, pen would add five times as much to her total utility as the last pencil. Lakshani has $50 per season to spend on tickets to football games and tickets to soccer games. Each football ticket costs $10 and each soccer ticket costs $5. She is thinking about buying 3 football tickets and 2 soccer tickets. Her marginal utility from the third football ticket is twice as much as her marginal utility from the second soccer ticket.

6.Cal “Cool” Cooper has $200 to spend on Nikes and sunglasses.

a. Each pair of Nikes costs $100 and each pair of sunglasses costs $50. Which bundles lie on Cal’s budget line? Draw a diagram like Figure 10-4 in which both the marginal utility per dollar spent on Nikes and the marginal utility per dollar spent on sunglasses are illustrated. Draw the quantity of Nikes increasing from left to right, and the quantity of sunglasses increasing from right to left. Use this diagram and the optimal consumption rule to decide how Cal should allocate his money. That is, from all the bundles on his budget line, which bundle will Cal choose? The accompanying table gives his utility of Nikes and sunglasses.

Quantity of Utility from | Quantity of Utility from a 2 Nikes (pair Nikes util | sunglasses sunglasses s) s) (pairs) (utils)

0 0 0 0 1 ‘400 2 600 2 700 4 700

b. The price of a pair of Nikes falls to $50 each, but the price of sunglasses remains at $50 per pair. Which bundles lie on Cal’s budget line? Draw a diagram like Figure 10-4 in which both the marginal utility per dollar spent on Nikes and the marginal utility per dollar spent on sunglasses are illustrated. Use this diagram and the utility-maximizing principle of marginal analysis to decide how Cal should allocate his money. That is, from all the bundles on his budget line, which bundle will Cal choose? The accompanying table gives his utility of Nikes and sunglasses.
Quantity of Utility from | Quantity of Utility from Nikes (pair Nikes (util s) wrro 4 s)
°
400 700 900 1,000 (pairs)
oO 1 2 3 4 (utils)
oO 325 600 825 700

c. How does Cal’s consumption of Nikes change as the price of Nikes falls? In words, describe the income effect and the substitution effect of this fall in the price of Nikes, assuming that Nikes are a normal good.