Problem 1.
Indicate whether the following statements are true, false, or uncertain. Explain your answers.
(a) A general rise in prices and income by the same percentage (e.g., prices and income increase by 10%), makes consumers better off.
(b) Equal "bang for the buck" means that the consumer equates the marginal utilities of all the goods he buys.
Problem 2.
Tizio, Caio, and Sempronio consume cheese (c) and salami (s). Their preferences can be described as follows. Tizio is always indifferent between an additional slice of salami and an additional slice of cheese. Caio, instead, likes to eat one slice of cheese with one slice of salami; extra slices of cheese (salami) without extra slices of salami (cheese) do not make him better off. Sempronio prefers balanced bundles of cheese and salami over unbalanced bundles; holding utility constant, the smaller the amount of salami, the greater the amount of cheese required to compensate for the loss of one slice of salami.
(a) Draw an indifference map for each consumer and discuss the shape of the indifference curves.
(b) Sempronio's preferences can be described by the utility function US (c, s) = cs, where c denotes slices of cheese and s denotes slices of salami. The price of a slice of cheese is 2 euro while the price of a slice of salami is 1 euro. Tizio, Caio, and Sempronio each have an income of 72 euro. Find each consumer's optimal consumption bundle and give a graphical representation of each consumer's optimal choice.
(c) How would Caio's optimal choice change if he liked to eat four slices of cheese with one slice of salami?
Problem 3.
Ronaldinho spends his entire weekly income of 200 euro on (bottles of) hair lotions (h) and (pairs of) soccer shoes (s). The market prices of these goods are ph = 10 and ps = 40. His utility function is given by U (s, h) = ln(h) + s.
(a) Write down Ronaldinho's budget constraint and the equation of the budget line.
(b) What is the optimal bundle of soccer shoes and hair lotion?
(c) How many pairs of soccer shoes is he willing to give up in exchange for a bottle of hair lotion at the optimal bundle?
(d) How would the optimal bundle change if Ronaldinho's weekly income suddenly fell to 140 euro?
Problem 4.
Repeat the previous exercise assuming Ronaldinho's utility function is U (s, h) = s + h.
Problem 5.
Giulia and Giacomo allocate their incomes between two goods: capelonghe (razor clams) and peoci (mussels). Both are purchasing positive amounts of both cape- longhe and peoci. Capelonghe cost 30 cents each and peoci cost 20 cents each. At Giulia's current levels of consumption, her marginal utility of capelonghe is 15 and her marginal utility of peoci is 5. The marginal utilities are 12 and 8, respectively, for Giacomo. Are Giulia and Giacomo maximizing utility? If not, should she/he buy more capelonghe or more peoci?
Problem 6.
Mr. Creosote has an 84 euro gift card which he can spend on mini muffins (M ) and large muffins (L). Mini muffins cost 1.50 euro and contain 45 calories. Large muffins cost 4.20 euro and contain 150 calories. Needless to say, Mr. Creosote maximizes caloric intake.
(a) Describe the set of bundles that Mr. Creosote can afford. Draw a few indifference curves and the budget line. How many muffins of each type will he buy?
(b) How would your answer change if the price of mini muffins fell to 1 euro. Use a diagram to illustrate your answer.
Problem 7.
Brad and Angie allocate their consumption between two goods: nuts and bolts. The price of nuts is 4 euros each. The price of bolts is 8 euros each. For Brad, the marginal utility of the last nut consumed was 8 and the marginal utility of the last bolt was 24. For Angie the marginal utility of the last nut was 6 and the marginal utility of the last bolt was 12. Which consumer is not maximizing his/her utility? How can you tell? How should he/she change his/her allocation?
Problem 8.
Suppose there are only two goods, x and y. The equation of a consumer's budget line is 4x + 8y = 120. Does the budget line become flatter or steeper when the price of good x changes to Px = 8?