S. Klepper, Economics 73-100, Fall 2008

Solutions to Exam I

1. Suppose there were 60 traders composed of 30 buyers and 30 sellers. The original demand and supply schedules are presented below. The equilibrium price was $2.50 and the quantity was 24 units, with 80% of both buyers and sellers making a transaction.

Original Schedules—Rounds 1 and 2

Price	Quantity Demanded	Quantity Supplied
$3.60	3	30
3.50	6	30
3.40	9	30
3.30	12	30
3.10	15	30
2.90	18	30
2.70	21	27
2.50	24	24
2.30	27	21
2.10	30	18
1.90	30	15
1.70	30	12
1.60	30	9
1.50	30	6
1.40	30	3

Consider the effect of the tax on the demand and supply schedules. Demanders have to earn at least $.20 in profit in order to be able to buy a unit. So if there redemption value was say $3.60, they could at most pay $3.40 for the good whereas in rounds 1 and 2 they would pay up to $3.60 for the good. For every buyer, the maximum price it would pay would decline by $.20. Now consider sellers, for example a seller with a cost of $1.60. Sellers also have to earn at least $.20 in profit. Hence a seller with a cost of $1.60 would have to sell his unit for at least $1.80 whereas in rounds 1 and 2 he would sell it at a price of $1.60. For every seller, the minimum price at which it would sell its unit would rise by $.20. The effect of these changes on the demand and supply schedules are presented below.
New Schedules—Round 3

Price	Quantity Demanded	Quantity Supplied
$3.60	0	30
3.50	0	30
3.40	3	30
3.30	6	30
3.20	9	30
3.10	12	30
2.90	15	27
2.70	18	24
2.50	21	21
2.30	24	18
2.10	27	15
1.90	30	12
1.80	30	9
1.70	30	6
1.60	30	3
1.50	30	0
1.40	30	0

The new demand schedule is such that the quantity demanded is lower at every price between $2.10 and $3.60 in round 3 than in rounds 1 and 2. The new supply curve is such that the quantity supplied is lower at every price between $1.40 and $2.90 in round 3 than rounds 1 and 2. The equilibrium price where the quantity supplied equals the quantity demanded is still $2.50, hence the price in round 3 will be the same as in rounds 1 and 2. But the quantity transacted is 21 units versus 24 units in rounds 1 and 2, hence the quantity transacted is less in round 3 than in rounds 1 and 2. Furthermore, three out of every 10 traders, or 30%, will not buy or sell a unit in round 3. These are the three demanders with redemption values of $2.10, $2.30, and $2.50 and the three sellers with costs of $2.50, $2.70, and $2.90. Among these traders, only the buyer and seller with a redemption value and cost of $2.50 transacted a unit in rounds 1 and 2, and both earned zero profits (excluding the commission). Consequently, their profits are no different in round 3 than in rounds 1 and 2. Among the other buyers and sellers in round 3, all buy and sell at the same price in round 3 as rounds 1 and 2 but have to pay the experimenter the tax of $.20, hence they all earn $.20 less in profits in round 3 than rounds 1 and 2.

Based on this discussion, the answers the individual questions, with the points allotted to them in brackets, are:

[4] 1. True

[4] 2. True

[7] 3. False

[6] 4. True

[6] 5. True

[7] 6. True

[6] 7. False

2. Consumers allocate their income so that marginal utility divided by price is equal for all goods. Therefore, if the price of food and shelter is the same, then the consumer must get the same utility from the marginal unit of food as the marginal unit of shelter. Consequently, the consumer would be willing to pay the same amount for the marginal unit of food and shelter. The consumer would also be indifferent between receiving another unit of food and another unit of shelter. We cannot infer anything about the total utility from food versus shelter. If the consumer’s income doubled, the consumer would not necessarily continue to spend half of his or her income on each good—it would depend on the consumer’s preferences.

Based on this discussion, the answers to the individual questions, with the points allotted to them in brackets, are:

[4] 8. False

[4] 9. True

[4] 10. True

[4] 11. True

[6] 12. False

3. If traders that began with 12 units of good X and 48 units of good Y could trade two units of Y for one unit of X, then their budget line would be the line in the figure below with intercepts of 36 for good X and 72 for good Y. The other line with X and Y intercepts of 60 represents their budget line in the version of the experiment conducted in class (rounds 1 and 2).

Traders Endowed with 12X and 48Y

Similarly, if traders endowed with 48 units of good X and 12 units of good Y could trade two units of Y for one unit of X, then their budget line would be the line in the figure below with intercepts of 54 for good X and 108 for good Y. The other line with X and Y intercepts of 60 represents their budget line in the version of the experiment conducted in class.

Traders Endowed with 48X and 12Y

The new budget lines of both traders cross their original budget lines. For the traders that began with 48X and 12Y, they could trade 18 units of good X for 36 units of Y, which would give them 30X and 48Y. Thus, one of the points on their new budget line would be (30,48), which implies that the point (30,30) is inside the budget line. This is the point that maximized the profits of traders in rounds 1 and 2 assuming a trading ratio of 1X for 1Y.

Traders who began with 48X and 12Y could trade 12X for 24Y and get to the point (36,36), which is on level 7. Consequently, they will attain a higher level than in rounds 1 and 2. In contrast, traders that began with 12X and 48Y will do worse in round 3 than in rounds 1 and 2. They could not benefit by trading units of good X for good Y as they would then end up with less than 12 units of good X and there is no point on level 2 or above with less than 12 units of good X. They could do better, however, by trading units of good Y for good X; for example, they could attain level 3 by trading 24 units of good Y for 12 units of good X, leaving them with 24 units of good X and 24 units of good Y. But they cannot get to any of the points on level 5 and so will get to a lower level in round 3 than rounds 1 and 2.

Traders will always want to trade until their willingness to pay for the marginal unit of good X (expressed in terms of units of good Y) equals the price of good X (in terms of units of good Y). With a trading ratio of two units of good Y for each unit of good X, the price of a unit of good X is two units of good Y. Hence both types of traders will want to trade until their willingness to pay for the marginal unit of good X equals two units of good Y.

Based on this discussion, the answers to the individual questions, with points allotted to the questions, are:

[4] 13. False

[4] 14. True

[4] 15. True

[6] 16. True

[5] 17. False

[4] 18. True

[5] 19. False

[6] 20. False