S.
Klepper, Economics 73100, Fall 2011
1. If labor is the only variable input and the amount of labor needed to produce each level of output declines by x%, then the total variable cost of each level of output will decline by x%. Then the average variable cost and marginal cost of each level of output will also decline by x%. Therefore, both marginal and average variable cost at every level of output will be at least 20% lower at the second plant than the first plant. If average variable cost is at least 20% lower at every level of output, then the minimum value of the average variable cost across all output levels must be at least 20% lower in the second plant than the first plant. Consequently, the minimum price at which producers would be willing to produce a positive level of output would be at least 20% lower in the second plant than the first plant. The total fixed cost and hence average fixed cost at every level of output would be the same in the two plants. At every level of output, average total cost equals average variable cost plus average fixed cost. With only average variable cost lower in the second plant than the first, the average total cost of the second plant at every level of output would not be 20% lower than the first plant if 20% less labor was needed to produce each level of output in the second plant than the first plant. Therefore, the average total cost of the second plant might be less than 20% lower than the average total cost of the first plant at each level of output.
Suppose labor is 20% more productive in the second plant than the first plant. Then the marginal cost schedules of the two plants in rounds 13 (multiply each by 10 for rounds 46) would be:
Output 
MC plant 1 
MC plant 2 



1 
6 
4.8 
2 
4 
3.2 
3 
2 
1.6 
4 
4 
3.2 
5 
6 
4.8 
6 
8 
6.4 
7 
9 
7.2 
8 
11 
8.8 
9 
13 
10.4 
Then the optimal choices in rounds 16 for plants 1 and 2 would be:
Round 
Price 
Q in plant 1 
Q in plant 2 
MC last unit, plant 1 
MC last unit, plant 2 






1 
3.50 
0 
4 
 
3.2 
2 
5.15 
4 
5 
4 
4.8 
3 
8.40 
6 
7 
8 
7.2 
4 
30 
0 
0 
 
 
5 
44 
4 
4 
40 
32 
6 
61 
5 
6 
60 
48 
The
new breakeven price would be $3.20 in rounds 13 and $32 in rounds 46. Consequently, in the second plant no output
would be produced in round 4 (if labor was only 20% more productive in the
second plant) but 4 units of output would be produced in round 1. Therefore, if
labor was only 20% more productive in the second plant, in one round it would
be profitable to produce a positive level of output in the second plant but not
the first. It would not, however, be
profitable to produce a positive level of output in the second plant in every
round. When it would be profitable to
produce a positive level of output in a plant, the output chosen would be where
the marginal cost of the last unit, as reflected above, is less than the price,
but the marginal cost of the next unit (not produced) is greater than the
price. Given the lower marginal cost at every output in the second plant, it
would always be profitable to produce at least as large an output in the second
plant as the first plant.
If
a positive level of output was produced in the first plant (and hence the
second plant), then at least as great an output would be produced in the second
plant. Then the profits earned from the
output produced in the second plant would exceed the profit earned from the
production of the output in the first plant. To see this, note that if the same
level of output were produced in the two plants, then it would be less
expensive to produce that output in the second plant and hence the profits
earned in the second plant would be greater than the profits earned in the
first plant. The only reason a greater level of output would be produced in the
second plant than the first plant is if even greater profits could be earned in
the second plant by doing so. Therefore, the profits earned in the second plant
would exceed the profits earned in the first plant if a positive level of
output were produced in both plants.
Note that in round 2 the marginal cost of the last unit of output
produced would actually be greater in the second plant than the first plant,
which results from the greater level of output produced in the second plant
than the first. Note that in this round,
4 units of output using 16 units of labor would be produced in the first plant
whereas 5 units of output using 17.6 units of labor would be produced in the
second plant. Consequently, it is
possible that more labor might be employed in the second plant than the first
plant.
Based
on this discussion, the answers to the individual questions, with points
allotted in brackets, are:
[3]
1. False
[5]
2. True
[5]
3. True
[5]
4. False—not if the labor saving was only 20%.
[4]
5. True
[6]
6. True
[6]
7. False
[6]
8. False
[7]
9. False
2. A theater cannot be maximizing its revenues if the quantity of tickets demanded at the price it charges is greater than the capacity of the theater; if it were then the theater could raise its price by some amount and still sell out the theater, thereby increasing its revenues. In general, setting a price at which the quantity demanded equals the capacity of the theater will not maximize its profits. To see this, suppose that at this price the price elasticity of demand were less than one. Then by raising its price, and in the process lowering the quantity demanded below the capacity of the theater, the theater would increase its revenues and hence its profits. More generally, if the price elasticity of demand were less than one then the movie theater could always increase its profits by increasing its price.
If a theater set a price such that the quantity demanded were less than the capacity of the theater and the price elasticity of demand were greater than one, it also could not be maximizing its profits. To see this, note that the theater could lower its price by some amount without the quantity demanded exceeding the capacity of the theater, and the revenues and profits of the theater would rise since the price elasticity of demand were greater than one. Last, the income elasticity of demand will have no bearing on the price that maximizes a theater’s profits since it does not indicate anything about how the quantity demanded is affected by the price charged.
Based
on this discussion, the answers the individual questions, with the points
allotted to them in brackets, are:
[4]
10. False
[3]
11. True
[5]
12. True
[3]
13. False
[5]
14. True
3. The annual growth in real GDP due to the growth in labor is computed as f * % annual growth in labor, where f is the fraction of GDP paid to labor, and the annual growth in real GDP due to the growth in capital is computed as (1 –f) * % annual growth in capital. Therefore, the growth in real GDP in both countries due to the growth in labor and capital was:
Chile: f_{C} * 8% + (1f_{C}) * 9%, where f_{C} is the fraction of GDP paid to labor in Chile
Brazil: f_{B} * 8% +(1f_{B}) * 12%, where f_{B} is the fraction of GDP paid to labor in Brazil
Regardless of f_{C} and f_{B}, the annual growth in real GDP due to the growth of labor and capital in both countries must have exceeded 8%. Furthermore, since f_{C} was greater than f_{B}, the annual growth in real GDP due to the growth in labor must have been greater in Chile than Brazil. Since both countries experienced the same annual growth in real GDP of 9%, a greater fraction of this growth can be attributed to the growth of labor in Chile than Brazil.
For Chile and Brazil, the residual annual growth in real GDP attributable to technical change was:
Chile: 9%  f_{C} * 8%  (1f_{C}) * 9%.
Brazil: 9%  f_{B} * 8%  (1f_{B}) * 12%.
Independent of the precise value of f_{C}, the residual annual growth in real GDP attributable to technical change must be between 0% and 1% for Chile, so some part of its growth is due to technical change. For Brazil, independent of the precise value of f_{B}, the residual annual growth in real GDP attributable to technical change must be less than 1% and could even be negative (which would occur if f_{B} was less than 3/4).
In the four Asian Miracle countries, the annual growth in real GDP attributable to technical change was estimated to range from 0.52% to 2.11% and averaged 0.705%. In both Chile and Brazil, the residual annual growth in real GDP attributable to technical change could have been less than 0.705% depending on the values of f_{C} and f_{B}. The average high income Western country was estimated to have a residual annual growth in real GDP attributable to technical change of over 1%, so regardless of f_{C} and f_{B}, both Brazil and Chile experienced a lower residual annual growth in real GDP attributable to technical change than the average highincome Western country. Since f_{C} is greater than f_{B} and both countries experienced the same annual growth in real GDP and labor but Brazil experienced a higher annual growth in capital, it must be the case that the residual annual growth in real GDP due to technical change over the past 15 years was greater in Chile than Brazil.
Based
on this discussion, the answers the individual questions, with the points
allotted to them in brackets, are:
[4]
15. True
[5]
16. True
[5]
17. False
[5]
18. True
[7] 19. True
[7] 20. False