Question

Dave enjoys cigars and whisky, which are denoted by ?c and ?w, respectively. He spends evenings relaxing in the backyard, smoking on a cigar and sipping on some whisky. But Dave is quite picky about having both goods together; he’ll never have whisky without a cigar or a cigar without whisky. That is, he needs to consume the two goods in a perfect one-for-one proportion. The price of a cigar is ??=40pc=40 and the price of whisky is ??=20pw=20. Dave’s income is ?=120m=120. For the questions below, treat cigars as the good that goes on the horizontal axis of an indifference curve diagram.

Part A. Solve for his optimal bundle of cigars and whisky, (?∗,?∗)(c∗,w∗). Show your solution graphically by placing cigars on the horizontal axis and whisky on the vertical axis. Label Dave’s optimal bundle as bundle “A” and be sure to label all intercepts of the budget line.

Part B. Dave’s friend, Brian, runs a very successful online sales company and cigars are Brian’s top seller! Brian offers to sell cigars to Dave at a lower price of ??=20pc=20. Solve for Dave’s new optimal bundle at these prices. Label it as bundle “C” and label all intercepts associated with the new budget line.

Part C. How does Dave’s optimal demand for whisky change when the price of cigars drops to $20? Are cigars and whisky substitutes or complements?

Answer 1

We know that for a consumer their optimal bundle of two goods with prices p1 and p2, and marginal utility mu1 and mu2 is: p1/p2 = mu1/mu2

we also know that marginal rate of substitution (MRS) is equal to mu1/mu2

In other words, the ratio of prices needs to be equal to the ratio of marginal utilities at the optimal bundle. Before or after this point, the consumer has an opportunity to increase their utility by changing teh bundle

In this case

assume p1 is along horizontal axis and p2 along vertical axis

p1/p2 = 6/9 = 2/3

and current MRS is 1/2, therefore the MRS needs to go up, which will happen if we move leftwards on the indifference curve, i.e., increase the quantity of x2 and reduce that of x1, but the quantities of both x1 and x2 will still be positive.

Hence the right answer is the second option: A positive amount of both ?1x1 and ?2x2