High School

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1. You have been given $100 to spend on milk and cookies. Milk costs $4 per carton and cookies cost $5 per box.

- Write down your budget equation.
- Graph the budget constraint, with milk on the horizontal axis and cookies on the vertical axis. Clearly label your graph, including intercepts.
- What is your opportunity cost of a box of cookies?
- Now suppose the price of milk decreases to $2 per carton. Draw your new budget constraint. Has the opportunity cost of cookies increased, decreased, or stayed the same?

2. Suppose you can work any number of hours you choose at $5 per hour and you have no income other than that which you earn by working. If you have zero income, the government pays you a welfare payment of $25 per day. You can receive your full welfare benefits so long as you earn no more than a total income of $5. For every dollar you earn beyond $5, the government reduces your welfare benefits by exactly the same amount until your welfare benefits drop to zero.

- Draw your budget constraint (with "Consumption" measured in $ on the vertical axis and Leisure on the horizontal axis) assuming that the most you can work per day is 8 hours.
- What is the opportunity cost of the 5th hour of leisure?
- How many hours are you likely to work? (This incentive scheme is similar to the AFDC (Aid to Families with Dependent Children) program that was abolished in 1997.)

3. Suppose you earn $2000 one summer, and spend all your money on tacos ($2 each) and iced coffees ($4 each). The next summer, you also spend all your money on those two goods, but the price of iced coffees has risen to $6. Despite this change, you notice that your budget constraint looks exactly the same as it did the previous summer.

- What is your new summer pay and what is the new price of tacos?

4. Draw your indifference curves between single cans of Coke and six packs of Coke.

- What is your marginal rate of substitution of single cans for six packs?

5. Suppose you have been dating someone for a little while and the conversation turns to your future and the prospect of a family. Your partner comes from a (very) large family, and that is reflected in their preferences over future family size. In particular, they mention that, all else equal, their ideal number of kids is 7, with their utility declining at an increasing rate as kids get farther from that number (above or below). Your partner also happens to mention that, without thinking about costs and independent of the number of kids they will have, they always prefer living in a larger house to a smaller house - the larger the better.

- On a graph of housing size (vertical axis) and number of kids (horizontal axis), draw a few indifference curves that represent your partner's preferences.

Answer :

i. Budget equation: 4M + 5C = 100; the opportunity cost of cookies decreases as milk price decreases, affecting both quantities.

ii. Budget constraint: $30, consumption varies with leisure time; opportunity cost of 5th hour $5, ranges from 0-8 hours.

iii. Individuals' income remains constant, iced coffee prices remain constant, and tacos remain affordable.

iv. Indifference curves show decreasing substitution rate between single cans and six packs.

v. Indifference curves show decreasing substitution rate between housing size and the number of kids, with an ideal number of kids indicating a preference for a larger house.

1. The budget equation is 4M + 5C = 100, where M represents the quantity of milk and C represents the number of cookies. The budget constraint graph shows a linear relationship with intercepts at (25, 0) and (0, 20). The opportunity cost of a box of cookies is 4/5 or 0.8 cartons of milk.

When the price of milk decreases to $2 per carton, the new budget constraint will shift outward, indicating a higher quantity of both milk and cookies that can be purchased. The opportunity cost of cookies will decrease.

2. The budget constraint in this scenario will be a horizontal line at $30, indicating that consumption can only vary with leisure time.

The opportunity cost of the 5th hour of leisure is $5, as the individual could have earned $5 by working during that hour. The number of hours the individual is likely to work will depend on their preference for leisure and the trade-off with earning income. It could range from 0 to a maximum of 8 hours.

3. Despite the increase in the price of iced coffees, if the budget constraint looks exactly the same as the previous summer, it means that the individual's income remains $2000 and the price of tacos remains $2 each. The change in the price of iced coffees does not affect the individual's purchasing power.

4. The indifference curves between single cans of Coke and six packs of Coke will slope downward, representing the diminishing marginal rate of substitution.

The marginal rate of substitution of single cans for six packs will depend on the individual's preferences and can be determined by the slope of the indifference curves at any given point.

5. On the graph with housing size on the vertical axis and the number of kids on the horizontal axis, the indifference curves representing the partner's preferences will be convex to the origin, indicating a diminishing marginal rate of substitution between housing size and the number of kids.

The curves will be highest and closest to the vertical axis at the ideal number of kids (7), reflecting the partner's strong preference for a larger house.

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