The Market

1. The Market Molly W. Dahl Georgetown University Econ 101 – Spring 2009

2. Economic Modeling • Construct a model • Choose simplifications • Solve the model • Come up with a prediction • Set S = D, etc. • Evaluate the model • Was it too simple? • Do we learn anything about the real world?

3. Modeling the Apartment Market • How are apartment rents determined? • Suppose • apartments are close or distant, but otherwise identical • distant apartments rents are exogenous (determined outside the model) and known • many potential renters and landlords

4. Modeling the Apartment Market • Who will rent close apartments? • At what price? • Will the allocation of apartments be desirable in any sense? • How can we construct an insightful model to answer these questions?

5. Economic Modeling Assumptions • Two basic assumptions: • Rational Choice: Each person tries to choose the best alternative available to him or her. • Equilibrium: Market price adjusts until quantity demanded equals quantity supplied.

6. Modeling Apartment Demand • Demand: Suppose the most any one person is willing to pay to rent a close apartment is $500/month. Then p = $500  QD = 1. • Suppose the price has to drop to $490 before a 2nd person would rent. Then p = $490  QD = 2.

7. Modeling Apartment Demand • The lower is the rental rate p, the larger is the quantity of close apartments demanded p   QD. • The quantity demanded vs. price graph is the market demand curve for close apartments.

8. Market Demand Curve for Apartments

9. Market Demand Curve for Apartments p QD

10. Modeling Apartment Supply • Supply: It takes time to build more close apartments so in this short-run the quantity available is fixed (at say 100).

11. Market Supply Curve for Apartments p 100 QS

12. Competitive Market Equilibrium • “low” rental price  quantity demanded of close apartments exceeds quantity available  price will rise. • “high” rental price  quantity demanded less than quantity available  price will fall.

13. Competitive Market Equilibrium • Quantity demanded = quantity available price will neither rise nor fall • so the market is at a competitive equilibrium.

14. Competitive Market Equilibrium p pe 100 QD,QS

15. Competitive Market Equilibrium • Q: Who rents the close apartments? • A: Those most willing to pay. • Q: Who rents the distant apartments? • A: Those least willing to pay. • So the competitive market allocation is by “willingness-to-pay”.

16. Comparative Statics • What is exogenous in the model? • price of distant apartments • quantity of close apartments • incomes of potential renters. • What happens if these exogenous variables change?

17. Comparative Statics • Suppose the price of distant apartment rises. • Demand for close apartments increases (rightward shift), causing • a higher price for close apartments.

18. Market Equilibrium p pe 100 QD,QS

19. Market Equilibrium p Higher demand pe 100 QD,QS

20. Market Equilibrium p Higher demand causes highermarket price; same quantitytraded. pe 100 QD,QS

21. Comparative Statics • Suppose there were more close apartments. • Supply is greater, so • the price for close apartments falls.

22. Market Equilibrium p pe 100 QD,QS

23. Market Equilibrium p Higher supply pe 100 QD,QS

24. Market Equilibrium p Higher supply causes alower market price and alarger quantity traded. pe 100 QD,QS

25. Comparative Statics • Suppose potential renters’ incomes rise, increasing their willingness-to-pay for close apartments. • Demand rises (upward shift), causing • higher price for close apartments.

26. Market Equilibrium p pe 100 QD,QS

27. Market Equilibrium p Higher incomes causehigher willingness-to-pay pe 100 QD,QS

28. Market Equilibrium p Higher incomes causehigher willingness-to-pay,higher market price, andthe same quantity traded. pe 100 QD,QS

29. Market Equilibrium p pe 100 QD,QS

30. Budget Constraints Molly W. Dahl Georgetown University Econ 101 – Spring 2009

31. Consumption Choice Sets • A consumption choice set is the collection of all consumption choices available to the consumer. • What constrains consumption choice? • Budgetary, time and other resource limitations.

32. Budget Constraints • A consumption bundle containing x1 units of commodity 1, x2 units of commodity 2 and so on up to xn units of commodity n is denoted by the vector (x1, x2, … , xn). • Commodity prices are p1, p2, … , pn.

33. Budget Constraints • Q: When is a bundle (x1, … , xn) affordable at prices p1, … , pn? • A: When p1x1 + … + pnxn£mwhere m is the consumer’s (disposable) income.

34. Budget Constraints • The bundles that are only just affordable form the consumer’s budget constraint. This is the set{ (x1,…,xn) | x1 ³ 0, …, xn³ 0 and p1x1 + … + pnxn=m }.

35. Budget Constraints • The consumer’s budget set is the set of all affordable bundles;B(p1, … , pn, m) ={ (x1, … , xn) | x1³ 0, … , xn³ 0 and p1x1 + … + pnxn£m } • The budget constraint is the upper boundary of the budget set.

36. Budget Set and Constraint for Two Commodities x2 Budget constraint is p1x1 + p2x2 = m. m /p2 x1 m /p1

37. Budget Set and Constraint for Two Commodities x2 Budget constraint is p1x1 + p2x2 = m. m /p2 x1 m /p1

38. Budget Set and Constraint for Two Commodities x2 Budget constraint is p1x1 + p2x2 = m. m /p2 Just affordable x1 m /p1

39. Budget Set and Constraint for Two Commodities x2 Budget constraint is p1x1 + p2x2 = m. m /p2 Not affordable Just affordable x1 m /p1

40. Budget Set and Constraint for Two Commodities x2 Budget constraint is p1x1 + p2x2 = m. m /p2 Not affordable Just affordable Affordable x1 m /p1

41. Budget Set and Constraint for Two Commodities x2 Budget constraint is p1x1 + p2x2 = m. m /p2 the collection of all affordable bundles. Budget Set x1 m /p1

42. Budget Set and Constraint for Two Commodities x2 p1x1 + p2x2 = m is x2 = -(p1/p2)x1 + m/p2 so slope is -p1/p2. m /p2 Budget Set x1 m /p1

43. Budget Constraints • For n = 2 and x1 on the horizontal axis, the constraint’s slope is -p1/p2. What does it mean?

44. Budget Constraints • For n = 2 and x1 on the horizontal axis, the constraint’s slope is -p1/p2. What does it mean? • Increasing x1 by 1 must reduce x2 by p1/p2.

45. Budget Constraints x2 Slope is -p1/p2 -p1/p2 +1 x1

46. Budget Constraints x2 Opp. cost of an extra unit of commodity 1 is p1/p2 units foregone of commodity 2. -p1/p2 +1 x1

47. Budget Constraints x2 Opp. cost of an extra unit of commodity 1 is p1/p2 units foregone of commodity 2. And the opp. cost of an extra unit of commodity 2 is p2/p1 units foregone of commodity 1. +1 -p2/p1 x1

48. Budget Sets & Constraints; Income and Price Changes • The budget constraint and budget set depend upon prices and income. What happens as prices or income change?

49. How do the budget set and budget constraint change as income m increases? x2 Original budget set x1

50. Higher income gives more choice x2 New affordable consumptionchoices Original and new budget constraints are parallel (same slope). Original budget set x1