GPP 501 Microeconomic Analysis for Public Policy Fall 2017

Transcription

1 GPP 501 Microeconomic Analysis for Public Policy Fall 2017 Given by Kevin Milligan Vancouver School of Economics University of British Columbia Lecture Sept 12th: Demand GPP501: Lecture Sept 12 1 of 24

2 Agenda for today: 1. Go from choice to preference maps. 2. Budget sets. 3. Demand Curves. GPP501: Lecture Sept 12 2 of 24

3 Axioms of choice: Reminder: why are we going through this? We want to build up to demand curves and supply curves. Once we understand demand and supply curves, we can start doing some economic analysis of policy issues. Q: do you remember the three from last lecture? Q: what did we say about choices that satisfied the three axioms? GPP501: Lecture Sept 12 3 of 24

4 Axioms of choice: From last time: 1. Completeness 2. Transitivity 3. Reflexivity Where do we want to go? We want to build a structure for preferences that we can represent in diagrams and in math. To do so, we will need to add more assumptions. GPP501: Lecture Sept 12 4 of 24

5 Axioms of choice: 4. Continuity: assumes that rankings are smooth A technical assumption that assures that preference rankings don t jump around the edges. This is necessary in order to write down preference curves. 5. Strong monotonicity: more is preferred to less. For any comparison, we assume that more is preferred to less. This can be weakened to local non-satiation. Necessary so that we don t have fuzzy or thick comparisons. 6. Convexity: assures well-behaved preference curves. Interior points on a line between two bundles are at least as good as boundary points. This one is much easier to see in a diagram.. GPP501: Lecture Sept 12 5 of 24

6 Indifference curves: x 2 Each indifference curve shows a constant level of enjoyment from bundles of x 1 and x 2. What does non-monotonicity do? What does convexity do? Can indifference curves cross? Which direction makes us best off? U2 o Is this true even for small jumps? U1 U0 x 1 GPP501: Lecture Sept 12 6 of 24

7 Exploring indifference curves: x 2 Does this violate any of the assumptions? How would you describe the way people like to consume x 1 and x 2? Any examples come to mind? U2 U1 U0 x 1 GPP501: Lecture Sept 12 7 of 24

8 Exploring indifference curves: x 2 Does this violate any of the assumptions? How would you describe the way people like to consume x 1 and x 2? Any examples come to mind? U2 U1 U0 x 1 GPP501: Lecture Sept 12 8 of 24

9 Agenda for today: 1. Go from choice to preference maps. 2. Budget sets. 3. Demand Curves. GPP501: Lecture Sept 12 9 of 24

10 Budget sets: We now know how to talk about choices over bundles of goods. Indifference, utility, preferences. But which bundle should we choose? What is our ultimate favourite bundle going to look like under strong monotonicity? What stops us from getting to that favourite bundle? GPP501: Lecture Sept of 24

11 Budget sets: Our model of choice is much more useful if we put a constraint on resources. Income Wealth Time We know time is a hard constraint; can t budge it. But income and wealth where do they come from? Complex choices about work, consumption, savings, human capital, and time. We ll just work with an endowment economy for now. Helicopter money. GPP501: Lecture Sept of 24

12 Budget sets: Imagine we have: Income set at fixed y. Goods x 1 and x 2. Prices for goods fixed at p 1 and p 2. Let s express this as a budget. y p 1 x 1 + p 2 x 2 All choices of bundles of x 1 and x 2 that satisfy the budget constraint are feasible choices. Q: Why did I use a sign? Q: Under what assumption would this hold strictly at =? GPP501: Lecture Sept of 24

13 Budget sets: What points can we afford? x 2 What points can we not afford? y = p 1 x 1 + p 2 x 2 x 1 GPP501: Lecture Sept of 24

14 Budget sets: x 2 y 0 < y 1 < y 2 What happens if I get more y? Parallel shifts outward of budget line. y 2 y 0 y 1 x 1 GPP501: Lecture Sept of 24

15 Budget sets: x 2 If you give up one unit of x 1 you are + p 1 dollars. y = p 1 x 1 + p 2 x 2 This means you can afford p 1 p 2 more units of x 2. So, the slope of the budget line is: Slope is p 1 p 2. x 2 x 1 = p1 p2 1 = p 1 p 2 x 1 GPP501: Lecture Sept of 24

16 Agenda for today: 1. Go from choice to preference maps. 2. Budget sets. 3. Demand Curves. GPP501: Lecture Sept of 24

17 Putting preferences and budget constraints together What happens when we combine our diagrams? Put down a given budget constraint. What is the best bundle we can afford? If we do this and then repeat the exercise for different prices of good x 1, we will trace out a demand curve for x 1. Let s give this a shot! GPP501: Lecture Sept of 24

18 Putting preferences and budget constraints together x 2 Start with our normal budget constraint. y = p 1 x 1 + p 2 x 2 Which points are feasible for us to pick? What points are not feasible? How should we choose among feasible points? x 1 GPP501: Lecture Sept of 24

19 Putting preferences and budget constraints together Consider A, B, C, D. x 2 Which is the point we like best if we could afford any of them? Considering our budget constraint, which should we choose? B C D What is true of the slope of the budget line and the slope of the indifference curve at the best point? A x 1 GPP501: Lecture Sept of 24

20 Let s redo it for different prices for x 1 : x 2 Start off at our initial price for x 1, price is p 1 0. We choose point C 0. Slope is p 1 p 2. Now increase the price to p 1 1 >p 1 0. C 2 C 1 C 0 We can afford less now, so budget constraint swings inward. We can only afford point C 1 now. That has less good x 1. Note that we can t necessarily say whether we consume more/less good x 2. x 1 Finally, tighten prices even more: p 1 2 >p 1 1. We now choose point C 2. GPP501: Lecture Sept of 24

21 Demand Curve for x 1 : p 1 Note that this is a different graph from the previous one. Previous one showed good x 1 and good x 2. C 2 This is just good x 1. C 1 C 0 x 1 GPP501: Lecture Sept of 24

22 Demand Curve for x 1 : p 1 What happens to demand curve if incomes go up? What happens to demand curve if price of other good goes up? o Does answer change for substitutes and complements? What happens to demand curve if price of good x 1 goes up? x 1 GPP501: Lecture Sept of 24

23 Concept: Elasticity of demand How can we characterize whether the change in demand when price changes is big or small? We use the concept of elasticity. We define it this way: Price elasticity of demand % X 1 % p1. What is the percentage change in the quantity compared to the percentage change in price? We generally use 1.0 as the cutoff between elastic and inelastic o If greater than 1.0, we call it elastic. o If less than 1, we call it inelastic. GPP501: Lecture Sept of 24

24 For next time We will move on to the other side: producers/supply. Homework: Watch this 9 minute youtube video GPP501: Lecture Sept of 24