Question

Theresa's weekly income is $11, price of a bagel is $2, and the price of a toy car is $1. What quantity of bagels and toy cars will maximize Theresa's utility if she spends her entire weekly income on bagels and toy cars? Explain your answer using marginal analysis.

Answer 1

You haven’t given Theresa’s marginal utility (MU) numbers, so there is not enough information to pick a unique bundle. The general rule (marginal analysis) is:

- Spend the next dollar on whichever good gives the larger marginal utility per dollar, MU/price.
- At an interior optimum (with positive amounts of both goods), MUbagel/Pricebagel = MUtoy/Pricetoy, i.e. MUbagel/2 = MUtoy/1.
- With a discrete budget, keep buying the unit (bagel or toy) that has the higher MU-per-dollar until you exhaust the $11.

Two simple special cases:
- If the marginal utility per physical unit is the same for bagels and toy cars (constant MU per unit), toy cars are cheaper ($1 vs $2), so buy 11 toy cars.
- If you know a MU schedule for each additional bagel and toy car, compute MU/2 and MU/1 for each successive unit and buy units in order of descending MU-per-dollar until the $11 is spent.

If you give the marginal utilities (or a utility function), I can compute the exact numbers of bagels and toy cars.