Some economists find experimental evidence of systematic differences between the amounts that people are willing to pay for an object and the amounts that they would have to be paid to give it up, if it is theirs. This is known as the “endowment effect.” Professor Daniel Mc- Fadden of the University of California devised a classroom experiment to test for an endowment effect. He randomly sorted students in a large class into two groups of equal size. Students in one group were given a pencil, embossed with the class name. McFadden then organized a pencil market. Each student who got a pencil was asked to write down the lowest price at which she would sell her pencil. Students without a pencil were asked to write down the highest price that they would be willing to pay for one. Students were told that the instructor would construct a “supply curve” by arraying the offers from low to high and a “demand curve” by arraying the bids from high to low. The equilibrium price is the price at which the supply curve meets the demand curve. Buyers who bid at least the equilibrium price would get a pen at the equilibrium price and sellers who offered to sell at prices at or below equilibrium would receive the equilibrium price for their pens. With these rules, it is in the interest of every student to bid his true valuation.
(a) McFadden noted that since students who received pencils were randomly selected, the distribution of willingness to pay for a pencil can be expected to be similar for those who were and those who were not given pencils. If there is no endowment effect, the lowest price at which a pencil owner is willing to sell her pencil is equal to the highest price that she would pay for a pencil. Since preferences in the two groups are approximately the same, we would expect that in equilibrium after the pencils are bought and sold, the number of pencils held by those who were not given pencils would be about equal to the number held by those who were given pencils. If this is the case, what fraction of the non-pencil-owners buy pencils? __________ What fraction of the pencil-owners would sell pencils? ____________ What fraction of the total number of pencils handed out would be traded? __________
(b) In Professor McFadden’s classroom, the number of pencils traded turned out to be much smaller than the number that would be expected without an endowment effect. An example will show how an endowment effect might explain this difference. Consider a classroom with 200 students randomly split into two groups of 100. Before pencils are handed out, the distribution of students’ willingness to pay for pencils is the same within each group. In particular, for any price P (measured in pennies) between 0 and 100, the number of students in each group who are willing to pay P or more for a pencil is 100−P. Suppose that there is no endowment effect. The demand curve of those without pencils is given by the equation D(p) = ____________ In the figure below, use black ink to draw the demand curve. The pencil-owners have 100 pencils. If they have the same preferences as the non-pencil-owners, then at price p, they will want to keep D(P) pencils for themselves. The number that they will supply is therefore S(P) = 100 − D(P). Substituting from the equation that we found for D(P), this expression simplifies to S(P) = _________ In the grid you find here, use blue ink to draw the supply curve. Supply equals demand when the price P is _________ and the number of pencils traded is ____________
(c) Suppose that there is an endowment effect that works as follows: Pencil-owners develop an attachment to their pencils once they get them. The lowest price that any pencil-owner will accept for her pencil is three times the amount that she was willing to pay before she got the pencil. On the figure, use red ink to show the supply curve for pencils, given this endowment effect. What is the equation for this red supply curve? S(p) = ____________ Assuming that the demand curve of non-pencil-owners does not change, what is the competitive equilibrium price for pencils? _____________What is the equilibrium number of pencils traded? __________