Question

Bongani budgets R600 for movies (M) and boxes of popcorn (B) per semester. He always buys one box of

popcorn with each movie ticket. The price of a movie ticket (PM) is R30 and the price of a box of popcorn
(PB) is R10.
a) At the top of a new page, draw a large and well-labelled diagram of Bongani’s budget constraint with
boxes of popcorn (B) on the horizontal axis and movies (M) on the vertical axis. [6]
b) Calculate and indicate the marginal rate of transformation on your diagram. [4]
c) Assuming he maximises his utility, how many boxes of popcorn and movie tickets will Bongani
purchase? [6]
d) Draw Bongani’s indifference curve and indicate his optimal bundle on your diagram. Comment briefly on
the shape of his indifference curve.

Answer 1

a) Budget Constraint

The budget constraint represents the set of all possible combinations of movies and popcorn that Bongani can afford given his budget of R600. Since he always buys one box of popcorn with each movie ticket, the budget constraint can be expressed as:

B = M + PB/PM

Substituting the prices, we get:

B = M + 10/30

Plotting this equation, we get the following budget constraint diagram:

b) Marginal Rate of Transformation (MRT)

The marginal rate of transformation (MRT) represents the trade-off between movies and popcorn. It is defined as the number of boxes of popcorn that Bongani must give up to get one more movie ticket.

To calculate the MRT, we can take the derivative of the budget constraint equation:

MRT = dB/dM = 1

This means that Bongani must always give up one box of popcorn to get one more movie ticket.

c) Maximizing Utility

Assuming Bongani maximizes his utility, he will purchase the combination of movies and popcorn that lies on his indifference curve and is also on the budget constraint. The indifference curve represents all the combinations of movies and popcorn that provide Bongani with the same level of satisfaction.

Since the MRT is constant, the indifference curve will be a straight line with a slope of -1. The optimal bundle will be the point where the indifference curve intersects the budget constraint.

d) Shape of Indifference Curve

The indifference curve is assumed to be convex to the origin. This means that as Bongani consumes more of one good, he needs to consume increasingly more of the other good to maintain the same level of satisfaction. This is because the marginal utility of each good diminishes as he consumes more of it.