Question

Suppose Bob is only willing to buy a bike seat if he can also buy a bike seat cover to go with it, i.e. Bob needs an equal number of bike seats and bike seat covers. Bob has $100 in income.

a. (10 points) Suppose bike seat covers cost $1 and bike seats cost $19. How many of each will Bob buy? Discuss and illustrate graphically.

b. (10 points) Suppose the price of bike seats increases to $49. How will Bob react to the price change? Discuss and illustrate on the same graph as in part a.

Answer 1

a) Since Bob has to buy a bike sear if he can also buy a seat cover. He has to buy equal number of both the goods. Bike seats and bike covers are complementary goods.

Cost of seat is $1 and cost of bike seat is $19.

His budget is 100$

Let x represent number of seats

y represent number of seat covers.

We have

19x + y = 100

Since it is given that x = y

we have 19x + x = 100

20x = 100

x = 5

Hence Bob can buy 5 seats and seat covers with his budget.

Note the indifference is shaped like that because the two goods are complementary in nature. i.e one cant derive the utility of other good if either is absent.

b) Suppose price of bike seat rises to $49

we have

49x + y = 100

since x = y

we have

50x = 100

x = 2

Hence he will buy 2 of each.

Since the price of seat has risen, the budget line shifts to the left and Bob is on a lower indifference curvve.

Bob will buy 2 of each since the price has risen.