Question

2. The Second Fundamental Theorem of Welfare Economics says that any point on the contract curve can be supported by a competitive equilibrium. This question has you illustrate and explain this argument. Start with an Edgeworth box diagram for a two-person, two good economy. In your diagram assume that there is a total of 100 units of food and 100 units of clothing which will be split between two people (Person A and Person B).

(a) Let’s say that the initial endowment is quite unequal giving Person A 90 units of both goods and Person B 10 units of each good. Illustrate this endowment point in the Edgeworth box.

(b) Say that if A and B trade from this endowment point they would trade to an efficient point where A has 95 units of clothing and 86 units of food while B has the remaining units of each good. Add indifference curves to your diagram in (a) to show this situation.

(c) Add a contract curve to your picture (note that it must go through the point Person A and Person B trade to in part (b)). Draw the contract curve so that it just happens to also go through the point where A has 50 of each good and B has 50 of each good.

(d) According to the Second Fundamental Theorem of Welfare Economics a government could use redistribution and markets to attain the outcome on the contract curve where each person gets 50 of each good. Explain how this could be done and illustrate.

Answer 1

a. The point I in the edgeworth box diagram shows the initial endowmenr where A has 90 units of both the commodities and B has 10 units of each commodity.

b. If A and B trade in such a way that A has 95 units of clothing and 86 units of food, then the B will have 5 units of clothing and 12 units of food at this point. This point is marked by S.

c. Contract curve is the locus of all the points of efficient allocations of two goods between two people. These points are attained through mutually beneficial trade of two commodities between two people and these points are pareto efficient. This is why all the points on the contract curve are those where the ICs of both the individuals are tangent to each other.

Also, the required point where every individual gets 50 units of each commodity is given by point M. Joining the points M and S, we get the contract curve (which is furthur extended to the origin of both the individuals).

d. The Second theorem of welfare says that any efficient allocation can be attained by a competitive equilibrium, given the market mechanisms leading to redistribution. Thus it separates distribution from efficiency.

Now, government can use redistribution and markets to attain point M. Since our initial endowment shows that A has more of both the goods, we can say that A is a resourceful person as compared B. Now the aim of the government is to make B better off using the market mechanism only. Here, the government can charge a lumpsum tax from A and then redistribute to B. We know that lumpsum taxes are not distortionary. Hence, the government has accompolished both the tasks. It has redistributed the resources in such a way that let the consumers to choose such points which are Pareto efficient. This is what the Second Welfare theorem states. (For more elaboration and examples, you can refer to any intermediate microeconomics book)