S. Klepper, Economics 73-100, Fall 2011

# Solutions to Exam I

1. If traders are offered a payment of \$.40 if they do not make a transaction, they will need to earn a profit of at least \$.40 in order to induce them to make a transaction.  Consider the effect this will have on suppliers.  In rounds 1 and 2, suppliers with a cost of \$1.40 were willing to sell their unit at a price of \$1.40 or above.  In round 3, they would not sell their unit at a price less than \$1.80. Similarly, suppliers with a cost of \$1.50 would sell their unit at a price of \$1.50 or above in rounds 1 and 2 but would require a price of at least \$1.90 to sell their unit in round 3.  In fact, the minimum price at which all sellers would be willing to sell their unit would rise by \$.40.  Now consider buyers.  The maximum price they would be willing to pay for a unit will decline by \$.40—for example, buyers with a redemption value of \$3.60 would buy a unit at a price of \$3.60 or less in rounds 1 and 2 but would not pay more than \$3.20 for a unit in round 3.

Consequently, the original and new supply and demand schedules are as follows:

Original Schedules

 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

New Schedules

 Price Quantity Demanded Quantity Supplied \$3.60 0 30 3.50 0 30 3.40 0 30 3.30 0 30 3.20 3 27 3.10 6 27 3.00 9 24 2.90 12 24 2.70 15 21 2.50 18 18 2.30 21 15 2.10 24 12 2.00 24 9 1.90 27 6 1.80 27 3 1.70 30 0 1.60 30 0 1.50 30 0 1.40 30 0

The new demand curve is such that the quantity demanded is zero at all prices above \$3.20.  The equilibrium price where the quantity supplied equals the quantity demanded is still \$2.50, hence the price in round 3 is the same as in rounds 1 and 2. But the quantity transacted is 18 units versus 24 units in rounds 1 and 2, hence the quantity transacted is 25% less in round 3 than in rounds 1 and 2.  Furthermore, four out of every 10 traders or 40% of the traders will accept the payment of \$.40 and won’t buy or sell a unit.  These are the four demanders with redemption values of \$2.10, \$2.30, \$2.50, and \$2.70 and the four sellers with costs of \$2.30, \$2.50, \$2.70, and \$2.90.  Among these traders, the buyers with redemption values of \$2.10 and \$2.30 did not buy a unit in rounds 1 and 2 and the sellers with costs of \$2.70 and \$2.90 did not sell a unit in rounds 1 and 2, hence all four of these traders will earn \$.40 more in profits in round 3 than rounds 1 and 2. On the other hand, the traders in round 3 all traded in rounds 1 and 2 and they trade at the same price as in rounds 1 and 2, hence their profits are the same in round 3 as 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. False

[6] 3. True

[5] 4. True

[5] 5. True

[4] 6. False

[7] 7. True

[7] 8. True

2.  If the price of clothing increased by 50%, then expenditures on clothing would increase by 50% if the consumer continued to purchase the same quantity of clothing.  If clothing initially accounted for half of the consumer’s expenditures, then the consumer would require ˝ of 50%, or 25%, more income to continue to purchase the same amount of clothing if the consumer continued to purchase the same amount of food.  Therefore, if the consumer’s income increased by 25%, the consumer would just be able to purchase the same quantity of clothing and food as previously.  This implies the new budget line must pass through the combination of food and clothing the consumer originally purchased.  With the price of clothing rising by a greater percentage than the rise in income and the price of food rising by a smaller percentage (zero) than the rise in income, the clothing intercept of the new budget line must be less than the clothing intercept of the original budget line and the food intercept of the new budget line must be greater than the food intercept of the original budget line.  This is pictured in the figure below.   The consumer originally consumed the combination of food and clothing denoted by (F0, C0), which lies on the original budget line.  The new budget line passes through this same point, with the food intercept of the new budget line greater than the food intercept of the original budget line and the clothing intercept of the new budget line less than the clothing intercept of the original budget line.

Since the budget lines cross, the consumer did not sustain an unequivocal rise in real income.  The consumer can consume the original combination of food and clothing, but with the change in the price of food relative to the price of clothing it will no longer be optimal to do so.  With food now cheaper relative to clothing, the consumer will increase the consumption of food and decrease the consumption of clothing.  Since the consumer could have chosen the old consumption bundle but chooses not to, the consumer must be better off.  In equilibrium, the marginal utility of food relative to the marginal utility of clothing must equal the price of food relative to the price of clothing. With the price of food relative to the price of clothing declining, the marginal utility of food relative to the marginal utility of clothing must be less than it was before the rise in the price of clothing and income.

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

[3] 9. True

[6] 10. True

[4] 11. False

[4] 12. False

[6] 13. True

[6] 14. 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] 15. False

[4] 16. True

[4] 17. False

[6] 18. False

[4] 19. True

[7] 20. False