Question

1. Bobby is a college student who has €500 of income to spend each semester on books and pizzas. The price of a pizza is €10 and the price of a book is є50. Suppose he consumes 20 pizzas. (a) Assuming that Bobby wants to maximie utility, draw Bobby's budget constraint and indifference curve. (b) Now, suppose Bobby's parents buy him a €300 gift certificate each semester that can only be used to buy You can assume that his indifference curves are regular (strictly convex) books, Draw Bobby's budget constraint when he has the gift certificate in addition to his є500 income. Is Bobby better-off with the gift certificates? Explain why/why not. (c) Using what you know about preferences, in general would a consumer prefer a 300 gift certificate or 300 in cash? Explain your answer using diagrams where possible.

Answer 1

Bobby consumes two goods - pizza and books.

Price of pizza = 10 and price of book = 50

Total income for Bobby = 500

Let amount of pizza and books consumed by Bobby be P and B respectively.

Thus, budget constraint: 10P + 50B = 500

Simplifying which we get: P + 5B = 50

a)

Utility will be maximized at the point where indifference curve is tangent to the budget line. Assuming indifference curves are strictly convex, such a point is unique. The situation can be explained from the following diagram.

→ UMP So,o)

b)

Let us assume that Bobby's parents has gifted him a gift certificate of 300 but it can be only used to spend on books.

Earlier, Bobby was consuming P = 20 and maximizing his utility.

Thus optimal amount of books bought can be found from the budget constraint (since Utility maximization point passes through both indifference curve and the budget line):

P + 5B = 50 => 20 + 5B = 50 => 5B = 30 => B = 6

After receiving the gift certificate of 300,

No. of books that can be bought from gift certificate = Total money/ cost of each book = 300/50 = 6

After receiving the gift certificate of 300, net income = 500 + 300 = 800 and the budget line shift outwards.

New budget line: P + 5B = 80

éui) ,N6) UMP So,0

Ideally the consumption of pizza and books should both increase and Bobby would move to a higher utility level if this entire 800 could have been spent on both the goods. But out of this, only 500 remains to be spend on pizza and 800 on books.

If Bobby still continues to consume only 20 pizza, his original UMP of 6 books can be achieved just with the remaining Budget and gift certificate is of no use to him.

However, since now with the additional income to be spent on books, Bobby could still buy even more than 6 books and have much more share left from his income to spend on pizza. Thus Bobby is better off with gift certificate in this case.

c)

A consumer would in general prefer 300 cash since this gives him more flexibility to find the unique utility maximization point by equating slope of indifference curves with the slope of budget line. There is less restriction on the maximum money to be spent on pizza (which was earlier 500 but now 800).

Thus a consumer is better off with 800 net income rather than a 300 gift certificate.