S. Klepper, Economics 73-100, Fall 2007

Solutions to Exam II

1. If an innovation reduced the amount of labor required to produce each unit of output by the same percentage, then the total variable costs of production at every level of output would fall by this percentage. For example, if the number of units of labor required to produce each level of output fell by 20%, the total variable costs of production at every level of output would fall by 20%. This would cause the marginal and average variable cost at every level of output to fall by 20% and it would have no effect on total fixed costs, implying that the average total cost at every level of output would fall by less than 20%. With average variable cost falling at every level of output, the minimum level of average variable cost would decline, causing the break-even price to decline. For example, if the innovation lowered the total amount of labor required to produce each unit of output by 20%, the minimum average cost would decline by 20%, causing the break-even price to decline to $3.20 in rounds 1-3 and $32 in rounds 4-6.

If the price of output were the same in every round, then in round 1 the price of output would have exceeded the minimum average variable cost and it would have been profitable for producers to supply a positive level of output, but in round 4 the price of output of $30 would still have been below the minimum average variable cost and it would not have been profitable to supply a positive level of output. Marginal cost would also have declined by 20% at every level of output if the innovation lowered the total amount of labor required to produce each level of output by 20%. This would have increased the profit-maximizing level of output in some rounds if the price of output remained the same in every round. For example, in round 3 it would have been profitable to produce a seventh unit of output since the new marginal cost of the seventh unit would be $7.20, which is less than the price of $8.40 in round 3. Furthermore, if the price of output were the same in every round, the profits of producers in rounds they produced would rise due to the decrease in total variable costs resulting from the innovation.

If the price of output decreased by the same percentage as the percentage fall in the total amount of labor required to produce each unit of output, then producers would not have changed their output in any round. Both average variable cost and marginal cost would fall by the same percentage as price in every round of the experiment. Then if the price were less than the minimum average variable cost before the innovation, causing producers to supply no output, it would still be less than the minimum average variable cost after the innovation, and hence it would still not be profitable to supply a positive level of output. Furthermore, if both marginal cost at every level of output and price fell by the same percentage, then the profit-maximizing level of output would be the same in each round. Thus, in every round producers would produce the same level of output. In rounds in which they produced a positive level of output, their revenues and total variable costs would both decline by the same percentage. Since in many rounds revenues exceeded total variable costs, the fall in revenues would exceed the fall in costs, which implies that the profits of producers would decline.

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

[3] 1. True

[5] 2. False

[5] 3. False

[4] 4. True

[5] 5. True

[6] 6. True

[7] 7. False

2. If the cost of projecting the movie is independent of the level of output of the movie, then the movie theater should choose a price that maximizes its revenues, subject to the constraint that revenues must be greater than or equal to the cost of projecting the movie. The distribution fee for the movie is irrelevant since theaters commit to paying this fee regardless of the popularity of the movie. The only thing that is relevant in terms of whether to show the movie is whether the revenues they can take in from ticket sales is greater than the costs of projecting the movie.

The 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 the 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 the 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:

[5] 8. False

[3] 9. False

[5] 10. True

[5] 11. True

[4] 12. False

[5] 13. True

3. The subsidy plan in which producers would be given a subsidy based on their level of output in the prior five years is equivalent to a lump sum payment that is independent of the level of output produced in the next year. This is equivalent to a reduction in fixed cost, with no effect on variable cost. This will have no effect on the marginal cost curve or the minimum average variable cost of production, but it will lower average total cost at every level of output. If minimum average variable cost is unchanged, then firms that were previously shut down will not open. If marginal cost is unchanged, then the short-run supply curve is unchanged and firms that previously produced will continue to produce the same level of output and the marginal cost of the marginal unit of output will be unchanged. The firms will increase their profits, though, by the extent of the subsidy.

The alternative plan lowers the total variable cost at every level of output next year by a percentage equal to the subsidy percentage. Therefore, this will lower marginal and average variable cost by this percentage at every level of output. Consequently, it will also lower the average total cost at every level of output. Because the average variable cost is lowered at every level of output, the minimum price at which producers will produce a positive level of output will decline. Because marginal cost is lower at every level of output, the subsidy will also cause the market supply curve to shift to the right. These changes are illustrated in the figure below. If price is unchanged at p₀, this will cause the quantity of steel produced to increase from Q₀ to Q₁ for those firms that were previously producing a positive level of output. The marginal cost of the marginal unit of output will equal the price and hence will be the same as last year. These firms will increase their profits since the government pays part of the cost of producing their old level of output and so they must earn greater profit on their old output, and they would produce additional output only if this increased their profits further. For firms that were not previously producing, if the subsidy is not large enough to lower the minimum average variable cost of production below the price, then they will not start producing and the subsidy will have no effect on their profits.

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

[5] 14. False—no firm will start producing under the first plan.

[5] 15. True

[5] 16. False—the market supply curve will shift to the right only under the second plan.

[5] 17. False—firm output would increase only under the second plan.

[5] 18. False—not if a producer remains shut down under the second plan.

[6] 19. True

[7] 20. True