Lecture 19 Monday, Oct. 1. Problem Set due tomorrow night.. At the course web site, I have posted some practice questions about consumer theory. I recommend taking a look at this. This material will be covered in discussion sections this week. Lecture 1 Indifference Curves: Perfect Substitutes. Indifference Curves: Fixed Proportions. Indifference Curves: Typical case of diminishing MRS. Change in income. Change in price.
Last class: Budget Constraint Suppose: Goldy has income: I = $ Price of pizza: P pizza = $ slice Price of beer: P beer = $ bottle 1 9 B8 e7 e r 1 0 Plot Budget Constraint 0 1 7 8 9 Pizza Slope = P pizza /P beer = / = is the opportunity cost of one more slice of pizza in bottles of beer
Budget constraint tells us what the consumer can do. What does the consumer want to do? Depends on the preferences of the consumer. Consumer will get different utility from different combinations of pizza and beer. Will make the choice that maximizes utility. We will call this choice the optimal consumption bundle. Going to go around. Assume the mascots consume only pizza and beer. All the mascots have the same income and face the same prices. But differ in preferences. We will explain their preferences and then look at their choices.
Case 1: Hawkeye (Perfect Substitutes) Hawkeye gets utility from calories (the more the better). Suppose pizza 00 calories and beer is 00 calories Calculate utility per dollar spent on each good: Pizza: Beer: Utility = 00*Q pizza + 00*Q beer What bundle maximizes utility? Remember P beer =, P pizza =. Beer is the best value (at these prices) in terms of utility per dollar spent. Hawkeye will spend all his money on beer. Q beer = Q pizza =
What is point of the picture? Gives us another way to figure out the optimal consumption bundle. Introduce concept of: Indifference curves: Combinations of beer and pizza that give the same utility (the consumer is indifferent. Aside: Indifference curves are all that matter. This utility function business just makes teaching this stuff easier. (Yes, easier!) Indifference curve through Q beer = and Q pizza = 0 Utility = 00*Q pizza + 00*Q beer Get 00 each way, so trade off one-for-one. 1 9 B8 e7 e r 1 0 0 1 7 8 9 Pizza
What about? Indifference curve through Q beer = and Q pizza = 0 Indifference curve through Q beer = and Q pizza = 0 Rule: pick the bundle on the budget constraint that gets to the highest indifference curve The slope of indifference curve is The Marginal Rate of Substitution Here one for one. (value of one more pizza slice in terms of beer). Look again at Q beer = and Q pizza = 0 On budget constraint: Value of one more unit of pizza: one beer Cost of one more unit of pizza: two beers
Case : Bucky Badger Fixed Proportions How many meals can he buy? Very particular: A meal: one beer and one pizza Utility equals number of meals. So Q pizza = and Q beer = in optimal consumption bundle. Suppose Bucky has I = just like before and P pizza = $ and P beer =$ What is optimal consumption bundle? How much for a meal?
Picture? 1 9 B8 e7 e r 1 0 0 1 7 8 9 Pizza Case : Goldy Gopher In between these extreme cases Diminishing marginal rate of substitution. Meaning, as he eat more pizza, his willingness to give up beer to get even more pizza goes down. Means indifference curves have a bowed shaped.
0 19 18 17 1 B9 e8 7 e r 1 0 U= U= 0 1 7 8 9 Suppose P Beer = $, P Pizza = $, I = $ At optimum two conditions: (1) On budget constraint and () P pizza MRS = P beer Marginal benefit of pizza (in beer) Marginal cost of pizza (in beer) =
Let s use the theory and look at the effect of an increase in income on demand. Suppose income increases from $ to $0. At Income = $: Pick optimal consumption bundle and label it A At Income = $0: Pick optimal consumption bundle and label it B 0 19 18 17 1 B9 e8 7 e r 1 0 U= U= 0 1 7 8 9 Pizza and beer are goods
Forget Beer and Pizza for now and let s suppose Spam and Steak are the only goods P spam = $, P steak = $ I = $ initially Spam 0 1 I = $0, new income 0 19 18 17 1 9 8 7 0 1 7 8 9 Steak
Effect of Price Change Complicated because two things going on: (1) opportunity cost going down () plus something like getting more income. Remember at I = $, P beer =$, P pizza = $ the optimal consumption bundle is Q beer =, Q pizza =. Suppose P pizza falls to $1. If stick with same consumption bundle than have *$=$9 extra in wallet. To understand how individuals react to a price change, economists break it down to two pieces: 1. Substitution effect. Effect of change in opportunity cost (by spending power held fixed so stay on same indifference curve). Income effect The effect of change in income holding opportunity cost fixed at the new level. But let s start with the total effect. That should be easy
I = $ and P Beer =$ fixed P Pizza = $: Label OCB A P Pizza = $1: Label OCB B 1 9 B8 e 7 e r 1 0 0 1 7 8 9 11718190 (OCB is Optimal Consumption Bundle) Movement A to B is total effect of price decrease Breakdown to substitution effect: New opportunity cost, but original indifference curve. Label this S Substitution Effect is movement from A to S Income Effect is movement from S to B Pizza