S.
Klepper, Economics 73-100, Fall 2009
Solutions to Exam I
In the third round, there would have been four buyers with each of the following combinations of redemption values for their two units:
Pairs of Redemption Values
for Buyers in Round 3
|
Unit 1 |
Unit 2 |
|
$3.60 |
$2.10 |
|
3.50 |
2.30 |
|
3.40 |
2.50 |
|
3.30 |
2.70 |
|
3.10 |
2.90 |
|
2.90 |
3.10 |
|
2.70 |
3.30 |
|
2.50 |
3.40 |
|
2.30 |
3.50 |
|
2.10 |
3.60 |
In the third round, there would also be four sellers with each of the following combinations of costs:
Pairs of Costs for Sellers in
Round 3
|
Unit 1 |
Unit 2 |
|
$1.40 |
$3.70 |
|
1.50 |
3.50 |
|
1.60 |
3.30 |
|
1.70 |
3.10 |
|
1.90 |
2.90 |
|
2.10 |
2.70 |
|
2.30 |
2.50 |
|
2.50 |
2.40 |
|
2.70 |
2.30 |
|
2.90 |
2.20 |
In terms of the number of units demanded at each price by the class, this is just twice the number of units demanded in rounds 1 and 2 of the experiment. Hence at a price of $3.60, eights units are demanded, at a price of $3.50 sixteen units are demanded, etc., all the way down to a price of $2.10, at which 80 units are demanded. This is represented in the schedule below, which summarizes the quantity demanded and supplied at each relevant price in round 3.
The situation on the supply side is a bit more complicated. The lowest cost of any unit is $1.40, and four units in total have a cost of $1.40 in round 3. The same is true for the costs $1.50, $1.60, $1.70, $1.90, and 2.10—there are four units at each cost in round 3. Thus, the quantity supplied at a price of $1.40 is four units, the quantity supplied at a price of $1.50 is eight units, and so forth up to a price of $2.10, at which the quantity supplied is 24 units. This is represented in the schedule below. The next lowest cost is $2.20 and there are four units at this cost in round 3, hence at a price of $2.20 the quantity supplied is 28 units. The next lowest cost is $2.30 and there are eight units at this cost in round 3, hence at a price of $2.30 the quantity supplied is 36 units. The quantity supplied at the other relevant prices is summarized in the supply schedule below.
Demand
and Supply Schedules for Round 3
|
Price |
Quantity Demanded |
Quantity Supplied |
|
|
|
|
|
$3.70 |
0 |
80 |
|
3.60 |
8 |
76 |
|
3.50 |
16 |
76 |
|
3.40 |
24 |
72 |
|
3.30 |
32 |
72 |
|
3.10 |
40 |
68 |
|
2.90 |
48 |
64 |
|
2.70 |
56 |
56 |
|
2.50 |
64 |
48 |
|
2.40 |
64 |
40 |
|
2.30 |
72 |
36 |
|
2.20 |
72 |
28 |
|
2.10 |
80 |
24 |
|
1.90 |
80 |
20 |
|
1.70 |
80 |
16 |
|
1.60 |
80 |
12 |
|
1.50 |
80 |
8 |
|
1.40 |
80 |
4 |
In rounds one and two no buyer would purchase a unit at a price above $3.60. The demand schedule for round 3 indicates the same is true for round 3, reflecting that $3.60 is still the highest redemption value for any unit. In rounds one and two every seller would sell a unit at a price of $2.90 or higher. The supply schedule for round 3 indicates that the same is not true for round 3, reflecting that the cost of some units in round 3 exceeds $2.90 and so a higher price is required for every seller to supply its two units. The schedules indicate that in round 3 the quantity supplied equals the quantity demanded at a price of $2.70, which is the equilibrium price in round 3. This compares with an equilibrium price of $2.50 in rounds 1 and 2. The quantity transacted is 56 units versus an equilibrium quantity of 32 units in rounds 1 and 2. Thus, the number of units transacted in round 3 is not twice as great as in rounds 1 and 2.
Every seller in round 3 has a cost for at least one of its units that is less than or equal to $2.70 and hence every seller would sell at least one unit in round 3. A seller would sell two units in round 3 only if the cost of both of its units was less than or equal to $2.70, which holds for four out of every ten sellers (see the pairs of costs for sellers above), or forty percent of the sellers. A buyer would buy two units in round 3 only if the redemption value for both of its units is $2.70 or greater, which holds for four out of ten buyers (see the pairs of redemption values for buyers above) or forty percent of the buyers.
Excluding the commission, the total profits earned by buyers in round 3 is not the same for all buyers. For example, at a price of $2.70 buyers with redemption values of $3.60 and $2.10 buy one unit and earn profits (excluding the commission) of $3.60 - $2.70 = $.90 whereas buyers with redemption values of $3.50 and $2.30 also buy one unit and earn profits of $3.50 - $2.70 = $.80. Similarly, excluding the commission sellers do not all earn the same profits in round 3. For example, sellers with costs of $1.40 and $3.70 sell one unit and earn profits of $2.70 - $1.40 = $1.30 whereas sellers with costs of $1.50 and $3.50 also sell one unit and earn profits of $2.70 - $1.50 = $1.20.
Last, consider the total profits of buyers. If the price were $2.50 in round 3 then buyers would buy twice as many units in round 3 as rounds 1 and 2 and would earn twice as much profit. But the price in round 3 is $2.70, which means that buyers earn less than they would have if the price had been $2.50. Consequently, they earn less than twice as much as in 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. False
[7]
4. True
[4]
5. True
[6]
6. False
[6]
7. True
[4]
8. False
[4]
9. False
[7]
10. False
2. If the consumer’s income increased sufficiently that the consumer could purchase the same combination of clothing and food that the consumer purchased ten years ago (the point C0, F0), then the current budget line must pass directly through the old combination of clothing and food purchased ten years ago, as pictured below. If the price of food increased by a greater percentage than the price of clothing and the new budget line passes through the combination of clothing and food purchased ten years ago, then the food intercept of the budget line must decline and the clothing intercept rise from ten years ago to today, as is also pictured below. Given that the budget lines cross, the consumer has not sustained an unequivocal change in real income from ten years ago to today. The consumer can be no worse off today than ten years ago since the consumer can still purchase today what he/she purchased ten years ago. However, given the price changes, it will no longer be optimal to consume the same combination of clothing and food that the consumer purchased ten years ago. With the price of clothing lower relative to the price of food today than ten years ago, the consumer would substitute clothing for food and in fact would be better off today than ten years ago.
Based on this discussion, the
answers to the individual questions, with points allotted in brackets, are:
[5]
11. True
[6]
12. True
[5]
13. False
[5]
14. False
[5]
15. False
3. If the price of tuition effectively declines, then individuals will consume more years of higher education and thus more individuals will go to college and less to (just) high school. The willingness to pay for the marginal unit of higher education will also decline as more education is consumed and it will end up equaling the lower price of higher education. The increase in the supply of college graduates will cause the wages of college graduates to decline, and the decrease in the supply of high school graduates will cause the wages of high school graduates to rise. This will reduce the difference in the earnings of college and high school graduates, thus contributing to a decline in income inequality.
Based
on this discussion, the answers to the individual questions, with points
allotted to the questions, are:
[4]
16. True
[5]
17. True
[4]
18. False
[4]
19. False
[5]
20. True