Exam 16: General Equilibrium

Any efficient allocation has to be such that everyone would agree to switch to that allocation from the endowment allocation -- or at least no one would object to such a switch.

If all goods are essential for everyone,efficiency requires that everyone get at least some of each good.

If the production technology in a Robinson Crusoe economy has increasing returns to scale,there is no production/consumption plan that is efficient.

If the two individuals' indifference curves through their endowment bundles are tangent to one another at the endowment bundle (in the Edgeworth Box),then the endowment bundle is a competitive equilibrium allocation.

If the production technology in a Robinson Crusoe economy has increasing returns to scale,there is not competitive equilibrium.

In and Edgeworth Box economy,no one strictly prefers the endowment allocation to the competitive equilibrium allocation.

Any allocation resulting from a mutually beneficial trade is efficient.

In the Edgeworth Box,we can set one price to 1 and only need to solve for the other price because only relative prices matter for individual choice when income is drawn from endowments.

If the two goods in an Edgeworth Box are perfect complements for one person and perfect substitutes for the other,then all efficient allocations are such that the first person has the same amount of good 1 as of good 2.

Comment on the following: "The second welfare theorem says that we can get any efficient allocation to be an equilibrium allocation.If endowments are inequitably distributed in an economy,we can therefore redistribute among people and still get an efficient outcome.As a result,there is no policy trade-off between equity and efficiency."

The second welfare theorem says that,regardless of how we redistribute endowments in an economy,we still get the same competitive equilibrium if markets are permitted to operate.

If the two goods in an Edgeworth Box are perfect complements for one person -- and if the other person has the typical tastes that satisfy our usual assumptions (without being extreme in any way),any efficient allocation will be such that the first person has equal amounts of good 1 and good 2.

If good 1 is essential for one person but not for the other,the first person will end up with all of good 1 in a competitive equilibrium within the Edgeworth Box.

If the two goods in an Edgeworth Box are perfect complements for both people,all efficient allocations will have each person getting the same amount of good 1 as of good 2.

Suppose we live in a 2-good Edgeworth Box economy and both of us have tastes that are quasilinear in good 1. a.Illustrate one efficient allocation in the Edgeworth Box. b.Where do the other efficient allocations that lie in the interior of the Edgeworth Box lie? c.It is typically the case that the contract curve goes from one corner of the Edgeworth Box to the other.Is that the case here as well?

Comment on the following: "The problem with models like the Edgeworth Box and the Robinson Crusoe economy is that it is silly to assume competitive behavior when there are so few individuals in the market."

Consider an Edgeworth Box economy with two individuals and two goods and suppose that the tastes of both individuals are quasilinear in good 1. a.Suppose initially that individual 1 has relatively little endowment of both good but the competitive equilibrium allocation has him consuming some of each.Illustrate such a competitive equilibrium. b.Now suppose the government is able to redistribute the endowment in this economy (prior to any trade occurring).In order to achieve a more equitable outcome,the government redistributes some of good 1 from individual 2 to individual 1.Show such a redistribution in your Edgeworth Box. c.Assume that both individuals continue to consume at an interior solution in the new equilibrium.How will the two individuals' consumption of good 1 change from what it would have been without the redistribution? d.Would your answer to (c)differ in any way if the government had instead redistributed good 2 from individual 2 to individual 1? e.How would a sufficiently large redistribution alter your answer?

A proof by contradiction can only be used to disprove a statement but not to prove a statement to be correct.

Suppose we live in an exchange economy with two goods.Together,we own 300 of good 1 and 300 of good 2.My tastes are captured by the utility function $u \left( x _ { 1 } , x _ { 2 } \right) = x _ { 2 } + 50 \ln x _ { 1 }$ and yours are captured by the utility function $u \left( x _ { 1 } , x _ { 2 } \right) = x _ { 2 } + 100 \ln x _ { 1 }$ . a.Calculate the portion of the contract curve that lies in the interior of the Edgeworth Box. b.Can you make intuitive sense of your answer?

Suppose we live in an exchange economy with two goods.I own 50 of both goods,and you own 250 of both goods.My tastes are captured by the utility function $u \left( x _ { 1 } , x _ { 2 } \right) = x _ { 2 } + 50 \ln x _ { 1 }$ and yours are captured by the utility function $u \left( x _ { 1 } , x _ { 2 } \right) = x _ { 2 } + 100 \ln x _ { 1 }$ . a.Calculate the competitive equilibrium price. b.How much do each of us consume of good 1 in equilibrium? c.Suppose the government transfers 100 units of your good 1 endowment to me.How is your answer to (a)and (b)affected? d.Suppose the government instead transfers 100 units of good 2 from you to me.How is your answer to (a)and (b)affected? e.Do you think your answers to (c)and (d)generally hold for most types of tastes -- or do you think they arise because of some specific feature of these tastes?