Intermediate Microeconomics with Calculus by Hal Varian Homework Midterm (50%) (11/10)

1. Intermediate Microeconomics with Calculus by Hal Varian • Homework • Midterm (50%) (11/10) • Final (50%) (1/12) • chenying@ntu.edu.tw, Mon 1:30-2:00 or by appointment (頤賢館757室) • Course TA 何宗祐, r02323005@ntu.edu.tw • Letter grades are relative as you will learn in this class only relative prices matter.

2. Initiative • 1 bonus point per class meeting (up to 16 bonus points) 蘋果橘子經濟學 超爆蘋果橘子經濟學 生命中的經濟遊戲 終結貧窮：可以在2025年以前達成 胖子的脂肪該被抽稅嗎？ • Cell phone

3. Chapter 1 The Market • A model of the apartment market in a college town • Every student needs one apartment. • All apts identical except: inner ring and outer ring • Focus on the market in the inner ring. • Assume the rent in the outer ring is fixed and in enough supply (the second best alternative).

4. Consider the demand curve (at every price, how many students would be willing to rent the apartments?). • When would a student be willing to rent one unit?

5. A price at which a student is indifferent between paying and living in the inner ring and renting an apt in the outer ring • Reservation price (a person’s maximum willingness to pay for something)

6. We can now draw the demand curve. • If a lot of persons, reasonable to assume smoothness • We see downward sloping and if goods are continuous, marginally indifferent between buying this extra amount and not (draw) • The idea of surplus

7. Fig. 1.1

8. Fig. 1.2

9. Turn to the supply curve • Landlords want to make as much profit as possible, so they jump in when renting and not renting yield equal profit. • Can similarly have a step-function-like supply curve • Assume in a short run, reasonable to have a vertical supply curve

10. Fig. 1.3

11. In continuous amounts, P=MC, marginally selling and not selling give the same profit • Similarly we have the idea of producer’s surplus. • Putting demand and supply curve together: get an equilibrium price p*

12. According to the market mechanism, who is willing to pay above p* gets to live in the inner ring. • Those who are not willing to pay as high as p* live in the outer ring. • Those who trade in the market all get some surplus (你情我願).

13. Equilibrium: at p* the number of people who are willing to rent (A) equals the number of apartments available for renting (B) • p>p*: A<B (surplus, incentives to lower the price) p<p*: A>B (shortage, incentives to raise the price)

14. Fig. 1.4

15. Comparative statics • (1) The university builds some new apartment. All these inner ring apartments are the same. • (2) Government passes a law that every landlord has to pay t<p* for every apartment he owns. (elasticity and tax incidence)

16. Fig. 1.5

17. Consider other ways to allocate apartments. • Discriminating monopolist (DM): a single seller who can perfectly discriminates by charging every consumer’s reservation price. Who gets the apartment? Still those whose reservation price is higher than p*.

18. Ordinary Monopolist (OM): a single seller who can only charge a price, so he maximizes pD(p). Suppose he therefore charges p’>p*. Those whose reservation price is higher than p’ get apts. • Rent Control (RC): pmax<p* to be effective We don’t know who gets the apt except their reservation price will be at least pmax.

19. Fig. 1.7

20. We now compare which is better. • Suppliers: DM > OM > Market > RC

21. Consumers: DM: indifferent to living in the outer ring OM: some surplus Market: more people with higher surplus RC: some with highest surplus, but some become indifferent to living in the outer ring

22. Pareto efficiency, due to Vilfredo Pareto (1848-1923): if there exists a way to make some better off without making anyone worse off, then it is a Pareto improvement. (皆大歡喜) • An allocation that allows for a Pareto improvement is Pareto inefficient while an allocation that does not allow for a Pareto improvement is Pareto efficient.

23. Suppose utility takes the form v I - p I if living in the inner ring; v O - p O if living in the outer ring. • Suppose we randomly assign people to live in the inner ring or outer ring and a person who is willing to pay 400 is assigned to the outer ring and another who is willing to pay 300 is assigned to the inner ring. • 400: v400, I – 400 = v400, O – pO 300: v300, I – 300 = v300, O – pO

24. Swap, the change of utility is: 400: (v400, I – pO) – (v400, O – pO) = 400 – pO 300: (v300, O – pI) – (v300, I – pI) = - (300 – pO) a transfer, say 350 – pO from the 400 person to the 300 person (黃牛票)

25. Market: Pareto Efficient (1st welfare theorem) • DM: Pareto Efficient (so efficiency says nothing about distribution)

26. OM: empty apts in the inner ring, not Pareto efficient. v200, I – 200 = v200, O – pO, move in, willing to pay up to (v200, I – pO)-(v200, O – pO)= v200, I –v200, O =200 – pO > 0, a transfer of (200 – pO)/2 to a landlord with an empty room in the inner ring would do. • RC: not Pareto Efficient

27. Remark • Model: not a one-to-one correspondence to reality • Endogenous variable and exogenous variable (demand curve, we control pO) (相關物品價格) • Optimization (U-max, profit max) • Equilibrium (behaviors consistent)