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ECO 4351 Prof. Millimet Problem Set #2. Answer Key. 1.

MRPE is the additional revenue from hiring one more unit of labor. It is equal to p MP E since MPE gives you the additional output produced by one more unit and multiplying this amount by P 

translates the output into dollar value. It is the …rm’s SR labor demand curve since it to maximize pro…ts, the …rm must equate unit and

w is the cost.

w and MRPE , since MRPE is the bene…t of the …rm to hiring another

The labor demand curve di¤ers for a monopolist since a monopolist does not

face a …xed price, but rather changes in a monopolist’s output change

p as well.

As a result, when

a monopolist hires another unit of labor, it produces more and lowers the price at which it can sell

MRPE , but now MRP E = MR MPE , MR is the marginal revenue obtained from producing another unit of output which re‡ects the fact that the additional output produced also changes the price. Since MR is less than the p, the all of its output. Therefore, a monopolist still cares about



where

labor demand curve for a monopolist is steeper and to the left of a competitive …rm’s labor demand.

2. Labor demand ... (a) In the short-run labor demand model from class,

K

K

is …xed in the short-run. As a result, a

change in the price of / will have no e¤ect on the short-run demand for labor. However, as shown in question 6 below, there is some inconsistency with what may happen in the short-run

K . There, if …rms react MC in the short-run, an increase in r will result in a reduction in labor demand in the short-run due to the higher MC of production. Either answer is acceptable as long as when we use the long-run demand model that incorporates the price of

to the change in

you are clear with your reasoning. (b) Lower demand will lower the price of the …nal good. A lower price lowers

MRPE , and, therefore,

shifts the labor demand curve in/down, resulting in a lower labor demand.

3. This is similar to how we derived an individual’s labor supply curve. Use the isoquant-isocost graph and vary the wage and trace out what happens to long-run labor demand. The output e¤ect is the short-run e¤ect on labor demand due to the change in output produced by the …rm (the movement from the old to the new isoquant in your notes), while the substitution e¤ect is the long-run e¤ect due to the substitution of capital for labor (the movement along the new isoquant in your notes).

1

4. The “3 for 10 rule” refers to the conventional wisdom of a short-run wage elasticity of labor demand of -0.3. In other words, if labor costs rise by 10%, labor demand falls by 3% on average. This is a short-run result; capital is …xed. In the long-run, empirical evidence indicates a “10 for 10 rule.” In other words, if labor costs rise by 10%, labor demand falls by 10% on average in the long-run. Thus, the long-run wage elasticity of labor demand is 1. 5. We did not talk about this, but L-shaped isoquants re‡ect inputs which are perfect complements. In this case, a drop in the wage rate has only an output e¤ect and there is no substitution e¤ect since in the long-run the only change is a decrease in capital demanded by the …rm, but no additional change in labor demand. So, there is no di¤erence between the short-run and long-run demand curves.

6. This just re-iterates the reasoning behind the long run labor demand curve being ‡atter than the short run demand curve. In the long run, a …rm can adjust their capital stock. Thus, in the long run auto makers will substitute away from more costly labor towards capital. The degree of substitution depends on the magnitude of the wage increase and the extent to which capital and labor are substitutes. 7. If the subsidy lowers the marginal cost of output immediately, then …rms are induced to produce a higher quantity. To expand in the short-run requires more labor since capital is …xed (A ! B). In the long-run, …rms substitute away from labor to the relatively cheaper capital (B ! C ). Thus, 2

labor increases in the short-run, with …xed capital; in the long-run, labor falls and capital increases. The net e¤ect on labor is ambiguous. Note, it is possible that …rms do not react to the change in the price of capital in the short-run since capital is …xed (thus, the change in price is irrelevant in the immediate future). In this case, nothing happens to capital or labor in the short-run. In the long-run, the …rm expands output and substitutes to cheaper capital, thereby jumping from

A!C

directly. Either answer is ‘correct’ as long as it is explained fully what you are assuming about …rm behavior.

8. “Robots and Jobs: Evidence from U.S. Labor Markets” ... (a) In theory, robots have two e¤ects on employment that go in opposite directions. The displacement e¤ect refers to the substitution from

L to K .

Speci…cally, some tasks that used to be

performed by humans are now performed by capital.

This reduces employment.

It re‡ects

the substitution e¤ect from class. The productivity e¤ect refers to more demand for

L to per-

form non-automatable tasks due to the desired increase in output resulting from the increase in productivity derived from automation. This is identical to the output e¤ect in the class notes. (b) The authors …nd a reduction in the employment-population ratio and wages in commuting zones exposed to greater adoption of robots. 9. “Will Automation Take Away All Our Jobs?” ... (a) The O-Ring theory of production conceptualizes production of a …nal good as depending on a series on intermediate steps, all of which are essential in the sense that if any step fails, then th entire production fails. (b) The O-Ring theory is one explanation for the so-called productivity e¤ect mentioned in the prior video. As robots make certain steps in the production process less likely to fail, then …rms are incentivized to invest more to make sure the remaining steps do not fail. This could lead to greater usage of

L in these other steps to make sure human error does not lead the entire

production process to fail.

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