S. Klepper, Economics 73-100, Fall 2007
Solutions to Exam III
1. The number of births in the U.S. fell from 1917 to 1937, and so the number of 20 year-old men born in the U.S. steadily declined from 1937 to 1957. With immigration closed off in the U.S. after 1929, the result was a steady rise in the wage rate of young men and consequently a steady rise in the fertility rate over the period 1937 to 1957. If immigration had not been closed off, the number of immigrants would have steadily risen from 1937 to 1957, which would have reduced the wage rates of young men and consequently the fertility rate would not have increased as sharply from 1937 to 1957. This in turn would have resulted in a less steep rise in the number of 20 year-old men from 1957 to 1977 and hence a less steep fall in the fertility rate in this period. In addition, immigration would have declined over the period 1957-1977, further dampening the rise in the number of 20 year-old men from 1957 to 1977 and the fall in the fertility rate.
In effect, not closing off immigration would have dampened the cycles in the number of 20 year-old men and hence would have dampened cycles in the fertility rate. The wage rates of 20 year-old men would also not have risen as sharply in the period 1937 to 1957, which would have caused the participation rate of 20 to 24 year-old women in the period 1945 to 1955 to decline less sharply (or even to rise). The less steep rise in the number of 20 year-old men from 1957 to 1977 brought about by immigration would also have caused the suicide rate of 15 to 24 year-old men to rise less sharply in the period 1957 to 1977. No change would have occurred in the suicide rate of men aged 55 to 64 during the period 1955 to 1977, as the youngest of these men (i.e., those age 55 in 1977) were born before the constraints on immigration would have been loosened. Consequently, their suicide rate would still have fallen over the period 1957-1977, reflecting the decline in the number of 55 to 64 year-old men during this period. No change would also have occurred in the percentage of 60 year-old women working from 1945 to 1955 as these women would have been married to men that were born before 1929 and hence would have been unaffected by the loosening of the constraints on immigration.
Based on this discussion, the answers to the individual questions, with points allotted to the questions, are:
[4] 1. True
[5] 2. True
[4] 3. False
[4] 4. False
[5] 5. True
[4] 6. False
2. Consider first the version of the experiment conducted in class. All the sellers were type 1. According to the model of perfect competition, the supply schedule of each seller was:
|
Price |
Quantity Supplied |
|
|
|
|
$.23 |
1 |
|
.34 |
2 |
|
.51 |
3 |
|
.69 |
4 |
|
.90 |
5 |
|
1.20 |
6 |
|
1.65 |
7 |
There were five sellers for every three buyers and the equilibrium price was $.51, with each seller selling three units of output and each buyer purchasing five units of output. In round 2, the minimum average cost of each seller was $.69, and the equilibrium price was $.69. At this price, each buyer purchased four units of output and each seller wanted to sell four units of output, with only 60% of sellers able to sell their desired four units of output and the other 40% of sellers exiting.
Now consider the modified version of the experiment. In round 1, the cost schedule of the type 2 suppliers is such that their supply schedule would be as follows:
|
Price |
Quantity Supplied |
|
|
|
|
$.34 |
1 |
|
.43 |
2 |
|
.51 |
3 |
|
.69 |
4 |
|
.74 |
5 |
|
1.10 |
6 |
|
1.50 |
7 |
Comparing this to the supply schedule of the type 1 suppliers presented above, the quantity supplied of type 1 and 2 suppliers is the same at a price of $.51. Therefore, at a price of $.51, both type 1 and type 2 suppliers would sell three units of output. Consequently, $.51 would still be the equilibrium price in round 1, and both types of sellers would sell three units of output and buyers would buy five units of output.
In round 2, the model of perfect competition predicts that the behavior of sellers depends on their minimum average total cost of production. Type 1 sellers have a minimum average total cost at four units of output of $.69. The total cost, marginal cost, and average total cost schedules of the type 2 sellers, including the $.99 payment as an opportunity cost, are as follows:
|
Unit |
Total Cost |
Marginal Cost |
Average Total Cost |
|
1 |
$1.33 |
$1.33 |
$1.33 |
|
2 |
1.76 |
.43 |
.88 |
|
3 |
2.27 |
.51 |
.7567 |
|
4 |
2.96 |
.69 |
.74 |
|
5 |
3.70 |
.74 |
.74 |
|
6 |
4.80 |
1.10 |
.80 |
|
7 |
6.30 |
1.50 |
.90 |
Ignoring the commission, the model of perfect competition predicts that in round 2 the type 2 sellers would supply no output at prices below $.74, which is their minimum average total cost of production. At a price of $.74 they would supply five units of output, where the marginal cost of the fifth unit equals $.74, and at higher prices they would supply at least five units of output. The commission on the fourth and higher units of output actually allows type 2 suppliers to make a total profit of $1.00 if they sold four units of output at a price of $.73, which exceeds the $.99 payment for selling no output in round 2, but they would be better off selling no output at a price below $.73. Therefore, if the price in round 2 were .$.69, as in the version of the experiment conducted in class, type 1 suppliers would be willing to supply four units of output and type 2 suppliers would supply no output. Each buyer would be willing to buy four units of output. There were five sellers for every three buyers. With 80% of the sellers type 1, there would be 4 type 1 sellers for every three buyers. Hence, at a price of $.69, the total quantity that all the type 1 sellers would want to supply would exceed the total quantity demanded. Since the quantity supplied would be zero at prices below $.69, the model of perfect competition predicts that in round 2 the price would still be $.69, with three out of every four type 1 sellers remaining in the market and the other 25% exiting the industry. Type 2 suppliers would supply no output, instead accepting the payment of $.99 not to sell any output in round 2. Excluding the commission, type 1 sellers would also earn $.99 in profit.
Based on this discussion, the answers to the individual questions, with the points allotted to them in brackets, are:
[5] 7. False
[5] 8. True
[4] 9. False
[4] 10. True
[5] 11. True
[5] 12. False
[7] 13. True
[5] 14. True
3. This problem is analyzed graphically in the figure below. If the government supplies 150,000 gallons of gasoline per day at the market price, in the short run the market supply curve of gasoline will shift to the right by 150,000 gallons at every price. This is represented below by the shift in the market supply curve from S0 to S1. The market demand curve for gasoline will not change. Consequently, as pictured in the graph the price of gasoline will fall in the short run. The quantity of gasoline sold will rise but by less than 150,000 gallons, as private refineries will decrease the quantity they produce in response to the decrease in price. In the short run, private refineries will also sustain a decrease in their profits due to the fall in price, hence they will earn negative economic profits.
In the long run, private refineries will exit due to earning negative economic profits. Since the average total cost of production of private refineries has not changed, exit will continue until the price rises back to its level prior to the government plan. Since the demand curve for gasoline has not changed, the quantity demanded and hence the total number of gallons of gasoline transacted will be the same as before the government plan.
Based on this discussion, the answers to the individual questions, with the points allotted to them in brackets, are:
[3] 15. False
[5] 16. True
[7] 17. False
[7] 18. True
[6] 19. False
[6] 20. True