- Budget constraint
- A budget constraint shows every combination of two goods a consumer can afford, given the prices of the two goods and the income there is to spend.
- Opportunity cost
- Opportunity cost is what a person must give up to obtain what they want: the value of the next best alternative.
What a shopper weighs at the margin
Can you name the three ideas that decide how a budget should be split?
At A-level the demand curve slopes down and firms stop where marginal cost equals marginal revenue. These three ideas give the household's version of that marginal rule, and with it the reason demand slopes down.
Marginal utility is the additional utility, or satisfaction, provided by one additional unit of consumption of a good.
Can you think of an example?
Going from two to three coffees a week raises your total satisfaction. The rise that comes from the third coffee alone is its marginal utility; the satisfaction from all three together is total utility.
Diminishing marginal utility is the pattern that, as a person receives more of a good, the marginal utility from each additional unit declines.
Can you think of an example?
The first slice of pizza brings more satisfaction than the sixth. That is why almost nobody spends a whole budget on one favourite thing, however much they like it.
Marginal utility per pound is the additional utility from one more unit of a good divided by that good's price.
Can you think of an example?
A £3 coffee that adds 9 utils gives 3 utils per pound. A £4 sandwich that adds 16 utils gives 4 per pound, so the next pound buys more satisfaction spent on the sandwich.
Check yourself
A coffee costs £3 and the last one you bought added 12 utils. A sandwich costs £4 and the last one added 12 utils. What should you do?
You enjoy coffee far more than sandwiches. With £24 a week to spend on the two, what does a rational shopper do?
Liking coffee more says which comes first, not how far to go. Each extra coffee adds less than the one before, so usually a pound on a sandwich soon adds more, and the shopper stops where the two are equal. Only if even the first sandwich adds less per pound than the last coffee does she buy coffee alone.
Start at AAt A most of the £24 goes on coffee: C0 coffees and S0 sandwiches, all on the budget line BL.
Moving along the budget line from A to E, coffees fall from C0 to C1 and sandwiches rise from S0 to S1, until each pound buys equal marginal utility.
- The line runs from £24 ÷ £4 = 6 sandwiches to £24 ÷ £3 = 8 coffees. Its slope is minus the price ratio, Pc ÷ Ps: each coffee costs three quarters of a sandwich.
- At A the last pound on coffee buys less marginal utility than a pound on sandwiches, so moving pounds from coffee to sandwiches raises total utility while spending stays at £24.
- As coffees fall the marginal utility of the last one rises, and as sandwiches rise theirs diminishes. At E the two are equal per pound: MUc ÷ Pc = MUs ÷ Ps, the consumer equilibrium.
BeforeOn BL1 the best choice is E1, with S1 sandwiches.
The sandwich price falls, so the budget line pivots out from BL1 to BL2 and the best choice moves from E1 to E2: sandwiches rise from S1 to S2.
- The coffee end stays put, since £24 spent only on coffee buys as many as before. The sandwich end moves out, from 6 to £24 ÷ £3 = 8, because each pound now buys more sandwiches.
- The line gets steeper: a cheaper sandwich means each coffee now costs a whole sandwich rather than three quarters of one. At E1 a pound on sandwiches now buys more marginal utility than a pound on coffee, so the choice moves towards sandwiches. Here coffee happens to stay at four; with other preferences it could rise or fall.
- A rise in income is different. It shifts the whole line out parallel to itself, because the price ratio, and so the slope, has not changed.
Check yourself
Your weekly income rises and the prices of coffee and sandwiches stay the same. What happens to the budget line BL1?
Doesn't the best choice give equal marginal utility from each good?
Only if the two goods cost the same. The rule is equal marginal utility per pound. If a T-shirt costs twice as much as a cinema ticket, then at the best choice the last T-shirt must bring exactly twice the marginal utility of the last ticket. If it brings less than twice, the T-shirt gives less satisfaction per pound, and switching money to tickets raises total utility. The same rule, written as ratios, says the ratio of the marginal utilities equals the ratio of the prices.
In an interview, draw the budget line before you talk about utility. Mark each intercept as income divided by that good's price, state the slope as minus the price ratio, then say how it moves: income shifts it parallel, one price pivots it. Then give the rule in words: spend so that the last pound on each good adds the same satisfaction.
Exam question
Water keeps us alive and diamonds do not, yet a diamond costs far more than a litre of water. How would an economist explain that? [4]
Price reflects marginal utility, not total utility. Water is so plentiful that people use it until the last litre does something trivial, such as rinsing a cup, so its marginal utility, and what they will pay for one more litre, is tiny. Diamonds are scarce, so the last one bought still adds a lot. Total utility from water is far higher. The answer assumes plenty of water: to someone lost in a desert, the next litre could be worth more than any diamond.
A strong answer names the model (marginal, not total, utility), applies it to both goods using diminishing marginal utility and scarcity, and ends with the case that breaks it, where water is scarce and its marginal utility soars.
Exam question
A friend says she always spends her money on whatever she likes most. Why might you tell her she is getting less from her money than she could? [4]
Liking one good most says nothing about the last pound. Because of diminishing marginal utility, each extra unit of her favourite adds less, so at some point a pound on something else adds more satisfaction. She gets the most from her budget when the marginal utility per pound is the same across everything she buys. The argument assumes she can buy in small steps and knows what each good adds; with a lumpy good, such as a holiday, she may not be able to equalise exactly.
The best answers move from what she likes most to what the last pound buys, state the equal marginal utility per pound rule, and then test its assumptions: divisible goods and a clear sense of the satisfaction each adds.
Exam question
Bus fares halve. Can you say for certain that a student who spends on buses and meal deals will buy more meal deals? [4]
No. With bus trips on the horizontal axis, the budget line pivots out along that axis and gets flatter, because a bus trip now costs fewer meal deals. Each pound on buses now buys more marginal utility than before, which pulls spending towards buses and away from meal deals. But the lower fare also leaves money over, some of which can go on meal deals. Which pull wins depends on her preferences, so meal deals could rise, fall or stay the same. If meal deals were an inferior good, both pulls would cut them.
Draw the pivot, then separate the two pulls: cheaper buses draw spending away from meal deals, and the freed-up money draws it back. Saying the result depends on preferences, and naming the normal-good assumption, is what an interviewer is listening for.
A budget constraint shows every bundle a consumer can afford. Its intercepts are income divided by each price and its slope is minus the price ratio. A rise in income shifts it out parallel; a change in one price pivots it. Because marginal utility diminishes, the best bundle is not all of the favourite good. The consumer picks the bundle on the line where the marginal utility per pound is the same for both goods.