MGEA02H3 Chap.3 Utility, Consumer Demand and Surplus
Utility, Consumer Demand and Surplus
From utility to demand
Utility in the course is measured in dollars, so consumer surplus is total utility minus spending. Maximising it gives the optimal purchase rule, marginal utility equals price, and so the marginal utility curve is the demand curve.
Diminishing marginal utility explains the law of demand, and market demand is the horizontal sum of individual demands.
Surplus and access pricing
Surplus can be computed as an area under demand or as U(X) − U(0) − PX, and both should agree.
Flat-fee questions compare the surplus from paying per unit with the surplus from consuming until marginal utility reaches zero, which gives the largest fee a consumer would accept.
What the answer keys reward
The keys reward three moves in order: differentiate utility correctly, applying the chain rule where quantity sits inside a bracket; set marginal utility equal to price; and compute surplus as U(X) − U(0) − PX.
For access-fee items they compute surplus under each plan and state the fee as the gap. They also insist that total utility is not consumer surplus and that marginal utility at the optimum equals the price.
How this topic connects to later chapters
Consumer surplus is the yardstick for every welfare claim that follows.
Chapter 4 measures how much of it a tax removes, chapter 8 counts it inside the gain to society under monopoly, and chapter 10 adds individual marginal utilities vertically to value a public good. The optimal purchase rule is also the first example of the marginal condition that recurs as P = MC and MR = MC.
What this chapter covers
- 01
Marginal utility as the derivative of utility
- 02
The optimal purchase rule MU = P
- 03
Consumer surplus as U(X) − U(0) − PX
- 04
Horizontal summation of individual demands
- 05
Flat fees and the maximum access charge
- 06
Kinked demand curves and split areas
Worked example · free
Gym visits priced per visit or by pass
- 2MU = 30 − 0.5X = 10 gives X = 40.
- 2U(40) = $800 and spending is $400, so surplus is $400.
- 2With a pass, X = 60 and U = $900, so the fee can be up to 900 − 400 = $500.
Key terms
- Marginal Utility
- Marginal utility is the extra dollar-valued benefit from one more unit, the derivative of total utility.
- Optimal Purchase Rule
- The optimal purchase rule says to buy until marginal utility equals the price.
- Consumer Surplus
- Consumer surplus is total utility from the units bought minus the amount paid for them.
- Law of Demand
- The law of demand states that quantity demanded falls as price rises, other things equal.
- Flat Fee
- A flat fee is a fixed access charge after which each extra unit costs nothing, so consumption continues until marginal utility is zero.
Utility, Consumer Demand and Surplus FAQ
Why is the marginal utility curve the same as the demand curve?
The consumer buys until marginal utility equals price. At every possible price, the quantity chosen is the one whose marginal utility matches that price, so plotting those pairs traces the marginal utility schedule itself.
When do I subtract U(0) in a surplus calculation?
Whenever the utility function has a constant term. Consumer surplus measures the gain from buying, so the part of utility that does not depend on purchases must be removed before subtracting spending.
How is market demand built from individuals?
Write each buyer’s demand with quantity on the left, add the quantities at each price, and then invert to price form. If buyers drop out at different prices, the market curve has kinks.
What does a zero consumer surplus tell me?
It means the consumer is exactly indifferent between buying the bundle and not buying it. The model cannot then predict whether the purchase happens, so an answer should say that the choice is undetermined rather than claiming the consumer buys or refuses.
Exam move
Take one utility function and compute quantity, total utility and surplus at two prices. Then price a flat fee for the same consumer and check the answer with the area under the demand curve. Rework at least one item where the utility function has a constant term and one with a fraction, since those are where most surplus mistakes appear.
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