Lecture 2(b) Rational Choice and Demand

Why It Would Probably Be Ok to Sleep Through This Part of the Lecture The previous lecture described almost everything you need to know to understand demand. You know what demand functions are about, what demand elasticity means and why it matters. The previous lecture described almost everything you need to know to understand demand. You know what demand functions are about, what demand elasticity means and why it matters. What comes next is a formalization of the theory of demand that doesn’t really extend your understanding of these things. What comes next is a formalization of the theory of demand that doesn’t really extend your understanding of these things.

But Why You Should Pay Attention Anyhow The previous lecture did not explicitly consider how a rational consumer would elect to act. This section will model rational consumer choice—the result of which is the demand for some goods. The previous lecture did not explicitly consider how a rational consumer would elect to act. This section will model rational consumer choice—the result of which is the demand for some goods. This is worth learning both to confirm the intuitive results from the previous lecture but, more importantly, to better understand the nature of optimization. This is worth learning both to confirm the intuitive results from the previous lecture but, more importantly, to better understand the nature of optimization. As an added bonus, this same model will be used when we look at production theory (hint: firms will be treated as “consumers” of inputs.) As an added bonus, this same model will be used when we look at production theory (hint: firms will be treated as “consumers” of inputs.)

Two Equivalent Ways to Describe What the Consumer Wants to Achieve Objective: Objective: Maximal happiness Maximal happiness Control variables Control variables Quantities of goods consumed Quantities of goods consumed Constraints Constraints Prices and income Prices and income Objective: Minimize Expenditure Control variables Quantities of goods consumed Constraints Achieve a “target level” of happiness

Modeling Preferences (The really tough part of the exercise since we’re actually trying to quantify something as complex as a consumer’s tastes) Marginal Rate of Substitution: The maximum amount of one good you would be willing to give up to get an extra unit of the other good Marginal Rate of Substitution: The maximum amount of one good you would be willing to give up to get an extra unit of the other good MRS = change Y/ change X (approximation) MRS = change Y/ change X (approximation) MRS = dY/dX (precise) MRS = dY/dX (precise)  The MRS is Often Best Understood by Imagining an “Indifference Curve”: Combination of Goods about Which The Consumer is Indifferent  MRS = slope of indifference curve (geometric)

Example: Suppose you’ve received five job offers to work for companies that offer some combination of two perks: Company Jet (let X = days per month) Golfing at Pebble Beach (let Y = days per month) and that you’re completely indifferent between each point (e.g., you are as happy with A as with B). OfferXYMRS A110 B26 4 C33 3 D41 2 E50 1

Optimization Problem Resolved Imagine the points in the previous example just represent 5 different packages, each of which contain different quantities of an X and Y. Imagine the points in the previous example just represent 5 different packages, each of which contain different quantities of an X and Y. Suppose also that the X good costs $5 and the Y good costs $2 Suppose also that the X good costs $5 and the Y good costs $2

Problem: Minimize the cost of achieving the level of “happiness” generated by one of the these five PackageXYMRSExpenditure A110 $ B26 4 $ C33 3 $ D41 2 $ E50 1 $ Package C Minimizes Expenditure

The Principle (Margins again): Think about the ratio of price as the marginal cost of one good expressed in terms of the other good (e.g., the marginal cost of x is 2 units of y). PackageXYMRSExpenditure A110 $ B26 4 $ C33 3 $ D41 2 $ E50 1 $ At these points the value of one more x is greater than the cost of one more X At the points the value of one more x is less than the cost of an x

Conclusion: The ideal choice for the consumer is one where the price ratio is as close as possible to the MRS Conclusion: The ideal choice for the consumer is one where the price ratio is as close as possible to the MRS Observations: Observations: It is easy to see that, at least most of the time, the law of demand holds—that is an increase in the price of x causes the consumer to buy less x. It is easy to see that, at least most of the time, the law of demand holds—that is an increase in the price of x causes the consumer to buy less x. Although there is an interesting exception that we’ll talk about if we have time. Although there is an interesting exception that we’ll talk about if we have time. The consumer problem is exactly the same as a firm trying to decide what mixture of inputs to buy in order to produce a certain amount of output. We’ll exploit this similarity in the next section. The consumer problem is exactly the same as a firm trying to decide what mixture of inputs to buy in order to produce a certain amount of output. We’ll exploit this similarity in the next section.