Question

A consumer has an income R. She can choose between two goods: wine and beer. Lets assume the price of a glass of wine (Pw) is three and the price of a glass of beer (Pb) is two. We denote the consumption of wine as Xw and the consumption of beer Xb Write the budget constraint of the consumer. Compute the slope of the budget line and represent it on a graph. The following tables give the different bundles of goods w and b, giving a utility level U(w,b) = 12.5, U(w,b) = 18 and U(w,b) = 24.5 (b) (4 points) Draw the three indifference curves. Given their shapes, would you say that wine and beer are complementary goods or substitute goods? What should be the impact of an increase of Pb on the demand for wine? (c) (4 points) Define and explain the concept of marginal rate of substitution. Com- pute the marginal rate of substitution if the consumer has the utility function of the form: U(Xw,Xb)=(Xw +4)(Xw +Xb) (d) (4 points) What is the value of the MRS at the optimum? What is the optimal bundle for this case? To reduce the public deficit, the government decided to double the tax on beer. Lets assume the price of beer goes from two to three. The price of wine remains the same. (e) (4 points) What is the new opportunity cost of a glass of beer? Using a graph, show the effect of this tax on the optimal decision of the consumer.

U(w, b)	Xw	Xb	U(w, b)	Xw	Xb	U(w, b)	Xw	Xb
12.5	0 0.5 1 1.5 2	3.1 2.3 1.5 0.8 0.1	18	0 0.5 1 1.5 2	4.5 3.5 2.6 1.8 1	24.5	0 0.5 1 1.5 2	6.1 5 3.9 2.9 2.1

Lets assume now that the consumer can choose between beer and champagne. The table below gives the optimal quantity of beer and champagne depending on the level of income.

R	Xb	Xc
0 4 8 12	0 3 1 0	0 1 2 6

(4 points) Draw the Engel curves for each of the goods. (g) (4 points) Given the shape of the Engel curves, what can you say about each of the goods? (h) (4 points) If the consumer’s income decreased because of the coronavirus crisis, what would happen to the demand for beer?

Answer 1