Intermediate Microeconomic Theory Exchange

Creating an Economy So far, we showed how an individual can potentially be made better off by a market, Market opens up the possibility of consuming preferred bundles to his or her endowment. What we have to consider however, is how market prices are determined. To do so, let us consider our desert island again. Al: endowed with wAc = 8 and wAm = 4. Bill: endowed with wBc = 4 and wBm = 6.

An Endowment Economy This means on the whole island, there are 8 + 4 = 12 gallons of coconut milk 4 + 6 = 10 lbs. of mangos. Consider first each person’s well-being in the absence of any market. Each person must simply consume his endowment. What is “wrong” with this allocation of island resources?

Edgeworth Box (Preferences) Are there feasible bundles that make both individuals better off? m 10 4 m 10 6 ICA ICB 4 12 c 8 12 c Al Bill

Edgeworth Box (Preferences) Are there feasible bundles that make both individuals better off? coconut milk for Bill coconut milk for Bill Bill m 10 4 m 10 4 4 c 12 4 Bill 6 10 m lbs. of mangos for Bill lbs. of mangos for Al lbs. of mangos for Bill 6 ICA ICA ICB ICB 8 12 c Al 8 12 c Al coconut milk for Al coconut milk for Al

Efficiency in an Endowment Economy Pareto Efficiency – There exists no allocation that makes at least one person better off without making anyone else worse off. Pareto Superior – An allocation that makes at least one person better off without making anyone else worse off. In Edgeworth Box, which allocations are Pareto Superior to allocation where each person consumes his endowment?

An Endowment Economy (Buying and Selling) What happens if there is a market where coconuts can be traded for mangos? Can this be Pareto Improving (i.e. make at least one of them better off while making no one worse off)? Suppose 1 gal. coconut milk can be traded for 1 lb. of mangos. How will this affect each person’s budget set? Prices: 1 coconut can be traded for 2 mangos If Al sold all 10 of his coconuts, he would have 4 + 20 = 24 mangos But there are on 14 coconuts total, so the most he could do is sell 5 coconuts and end up with 4 + 10 = 14 mangos and 5 coconuts If Al sold all 4 of his mangos, he would have 10 + 2 = 12 coconuts and have zero mangos Prices: 2 coconuts for 1 mango If Al sold all 10 of his coconuts, he would have 4 + 5 = 9 mangos If Al sold all 4 of his mangos, he would have 10 + 8 = 18 coconuts However, since there are only 14 coconuts total, the most he could do is to sell 2 of his mangos, giving him 10 + 4 = 14 coconuts and 2 mangos.

Edgeworth Box (Budget Sets) Consider a market where 1 lb. mango must be traded for 1 gal. coconut milk (coconut milk is numeraire and pm = 1) m 10 5 4 m 10 6 5 m 10 5 4 Bill 10 5 4 5 6 4 5 10 12 c 2 7 8 12 c Al 2 7 8 12 c Bill Al

Edgeworth Box (Budget Sets) How do things change when 1 lb. of mango costs 2 gal. of coconut milk (pm = 2)? m 10 8 5 4 2 m 10 8 5 4 2 m 10 8 6 5 2 Bill 2 5 6 8 6 4 So if 2 coconuts can be traded for one mango, the Al could trade 2 of his mangos for 4 more coconuts (for a total of all 14) Al could trade all 10 of his coconuts for 5 more mangos (for a total of 9) Bill could trade 5 of his mangos for 10 more coconuts (giving him all 14 coconuts) Bill could trade all 4 of his coconuts for 2 more mangos (giving him a total of 12 mangos) 4 6 12 c 6 8 12 c Al 6 8 12 c Bill Al

Edgeworth Box (Budget Sets) So like with Buying and Selling, change in price simply rotates budget constraint around endowment point. m 10 8 4 2 m 10 8 4 2 m 10 8 6 2 Bill 2 6 8 10 4 So if 2 coconuts can be traded for one mango, the Al could trade 2 of his mangos for 4 more coconuts (for a total of all 14) Al could trade all 10 of his coconuts for 5 more mangos (for a total of 9) Bill could trade 5 of his mangos for 10 more coconuts (giving him all 14 coconuts) Bill could trade all 4 of his coconuts for 2 more mangos (giving him a total of 12 mangos) 4 10 12 c 8 12 c Al 8 12 c Bill Al Rise in price of mangos (in terms of coconut milk) flattens B.C.

Equilibrium Prices The key question then is what prices can be maintained in an equilibrium?

Equilibrium Prices Consider Al and Bill. Al: uA(qc,qm) = qc0.5qm0.5 wAc = 8 wAm = 4 Bill: uB(qc,qm) = qc0.5qm0.5 wBc = 4 wBm = 6 In equilibrium, can price pm = 1 (where pc implicitly equals 1)? What is Al’s budget constraint? Bill’s? How much coconut milk will Al demand? How about Bill? How much mango will Al demand? How about Bill?

Gross Demands in an Edgeworth Box 10 4 Al qBc(1, 4, 6) = 5 6 4 Bill qBm(1,4,6)=5 So at these prices there is an excess demand for coconuts and an excess supply of mangos! What has to happen to prices to equate demand and supply? Price of coconuts must rise relative to the price of mangos. What will this do to budget constraint? Steepen it! qAm(1,8,4)=6 8 12 c qAc(1, 8, 4) = 6

Gross Demands and Equilibrium So at prices pm = 1 and where pc =1 (i.e. when 1 lb. of mangos can be traded for 1 gal. of coconut milk ), there is: A excess demand for mangos (6 + 5 = 11 lbs. are demanded, but only 10 lbs. exist) A excess supply of coconut milk (6 + 5 = 11 gallons are demanded, but 12 gallons exist). Equilibrium prices must be market clearing, or equate demand with supply.

Equilibrium Prices So Equilibrium prices {pc* ,pm*} are such that: qcA(pc* ,pm*, 8, 4) + qcB(pc* ,pm*, 4, 6) = 8 + 4 qmA(pc* ,pm*, 8, 4) + qmB(pc* ,pm*, 4, 6)= 4 + 6 What are the demand functions for each good for Al and Bill given arbitrary prices? How do we use these demand functions to find the (relative) prices that can be maintained in equilibrium? Al’s endowment of coconut milk Bill’s endowment of coconut milk Al’s endowment of mangos Bill’s endowment of mangos

Gross Demands in Equilibrium 10 4 Al qBc(1, 4, 6) = 5.6 6 4 Bill qBm(1,4,6)=4.66 So at these prices there is an excess demand for coconuts and an excess supply of mangos! What has to happen to prices to equate demand and supply? Price of coconuts must rise relative to the price of mangos. What will this do to budget constraint? Steepen it! qAm(1,8,4)=5.33 8 12 c qAc(1, 8, 4) = 6.4

Equilibrium Prices So in equilibrium, a pound of mangos cannot be obtained for 1 gal. of coconut milk. Rather, 6/5 gal. of coconut milk must be traded for a pound of mangos. Why is this the case?

Equilibrium Prices This reveals an important property of equilibrium prices. They serve as a way of rationing finite resources. Does this rationing mechanism (i.e. a market) lead to a Pareto improving allocation in equilibrium? What will be true at a Pareto Efficient allocation? Does market lead to Pareto Efficient allocation?

Markets and Efficiency First Welfare Theorem – Under Perfectly competitive markets, all market equilibria are Pareto Efficient regardless of initial distributions of resources (i.e. endowments) While distribution of initial resources does not affect efficiency of market allocation, it will affect equity. Show Graphically!

Equity and Efficiency in an Edgeworth Box m 10 7 Al 2 Bill 3 So even though market makes both Al and Bill better off, if initial allocation is very unequal, market allocation may also be unequal. 10 12 c

Equity and Efficiency in the Market So while efficiency is one criteria for a “good” allocation, another criteria might be that it meets certain equity principles. Are these goals always in conflict? Not necessarily Consider all the possible Pareto Efficient Allocations (contract curve). Which of these allocations can be maintained in a market equilibrium given appropriate redistributions of endowments?

Equity and Efficiency in an Edgeworth Box m 10 7 5 Al 7 2 Bill 3 5 contract curve How can this allocation be supported in a market equilibrium? 5 10 12 c

Equity and Efficiency in an Edgeworth Box m 10 7 Al 7 2 Bill 3 5 5 How can this allocation be supported in a market equilibrium? Reallocate endowments to this allocation, then find equilibrium price. 10 12 c 5

Equity and Efficiency with Re-distribution Second Welfare Theorem – (If all individuals have convex preferences) There will always be a set of prices such that each Pareto Efficient allocation can be maintained in a market equilibrium given an appropriate re-distribution of endowments.

Discussion of Welfare Theorems First Welfare Theorem Reveals that markets can provide a mechanism that ensure Pareto Efficient outcomes, even if any given individual’s information is very limited. Second Welfare Theorem Reveals that issues of efficiency and distribution can potentially be separated. Society can decide on what is a just distribution of welfare, and markets can potentially be used to achieve it. In other words, markets can potentially be part of the solution to achieving a “more just” distribution of welfare. Market prices should be used to reflect relative scarcity, Endowment/Lump-sum transfers should be used to adjust for distributional goals. John Rawls “Behind the Veil” Reveals that markets can provides a mechanism that ensure Pareto Efficient outcomes, With only two people, this wouldn’t be too difficult of a problem. But with thousands, or millions, obviously determining a Pareto efficient allocation is complicated. With markets, no individual needs very much information to get resources allocated to a Pareto superior allocation. A person only needs to know his preferences and prices. Under a well functioning market, competitive prices will be sufficient to achieve an efficient allocation.

Efficiency in a Market with Production Now, suppose that instead of simply being endowed with coconut milk or mangos, Al and Bill had to produce them. In particular, suppose each of their production possibilities sets are given below (i.e. all the bundles they could produce). What does curvature of each individual’s production frontier imply? What does comparing intercepts across individuals reveal? mangos 8 mangos 12 Bill Al 12 coconut milk 8 coconut milk

Efficiency in a Market with Production In absence of trade, production possibility sets are effectively each person’s budget set. Therefore, in absence of trade, each person picks the bundle in production possibilities set/budget set that gets him to highest I.C. So in the absence of trade, a total of 5 + 2 = 7 lbs. of mangos and 3 + 4 = 7 gal. of coconut milk will be produced and consumed. Neither person specializes! mangos 8 2 mangos 12 5 Bill Al 3 12 coconut milk 4 9 coconut milk

Efficiency in a Market with Production Note that without a market, neither person would choose to specialize in only producing one thing since they like to consume both. The Edgeworth Box view of this non-trade world is depicted below. However, while Al has an absolute advantage in both goods, Bill has a comparative advantage in producing coconut milk. mangos 12 5 Bill 4 2 Al 3 7 9 12 coconut milk

Efficiency in a Market with Production Therefore, suppose Bill specializes in producing coconut milk, Al specializes in producing mangos, and then both trade. With specialization, a total of 12 lbs. of mangos and 9 gal. of coconut milk will be produced and consumed. without trade and specialization with trade and specialization mangos 12 mangos 12 5 9 4 Bill Bill 4 2 2 5 Al 3 Al 3 7 9 12 coconut milk 9 coconut milk

Efficiency in a Market with Production Adam Smith’s “Invisible Hand” “It is not from the benevolence of the butcher, the brewer, or the baker, that we expect our dinner, but from their regard to their own interest. We address ourselves, not to their humanity but to their self-love, and never talk to them of our necessities but of their advantages.” Relatedly, William Easterly relates the old joke: “Heaven is where the chefs are French, the police are British, the lovers are Italian, the car mechanics are German, and it is all organized by the Swiss. Hell is where the chefs are British, the police are German, the lovers are Swiss, the car mechanics are French and it is all organized by the Italians.” Specialization doesn’t necessarily involve innate abilities. Rather each person (or country) does a task repeatedly and practice makes perfect. We can then trade this greater number of products that arise through specialization and all become better off.

Why Can the Welfare Theorems Fail? Welfare Theorems are why “free market” policies are often imposed on developing or transitioning economies as a pre-condition to aid. Problem: Well functioning markets are not assured. Numerous conditions are necessary for markets to function well. What does Easterly highlight in “You Can’t Plan a Market”? Other Limitations? What if agents act strategically rather than as price takers? What if one person’s consumption affects another person’s utility or one firms production affects another firm’s costs?