Econ402:Labor Economics

                                                                                       Mr. Killingsworth

MIDTERM EXAM

INSTRUCTIONS:  Answer any four of the six questions below.  (If you answer more than four, your best four answers will determine your exam grade.)  Read each question carefully to make sure you understand it. Your answers should be based on the lectures, readings, etc., that you have studied in this course.   Explain each answer; make sure it responds directly to the question that has been asked.

When you are finished, please fold this exam paper in two, put it inside your bluebook and hand them both in.

1. Jane Jones is working 37 hours per week at a wage rate W of $20 per hour.  She receives non- work income V of $14 per week, and purchases a single consumer good C whose price P is $10 per unit. She regards both the consumer good C and leisure time L as "normal" goods.  Suppose that the wage rate W rises from $20 to $30, and, at the same time, the price of consumer goods P rises from $10 to $15. Given this information, is it possible to say whether her hours of work per week will increase, decrease, or remain the same?  Explain your answer.  (Hint: Draw a picture!)

2.  The ABC Co. operates under conditions of increasing marginal cost (MC) using inputs of both capital (K) and labor (E), whose prices are R and W, respectively. The wage rate, W, falls.

A.         Under what conditions, if any, will this fall in W result in an increase in the demand for labor, E? Explain your answer.

B.         Under what conditions, if any, will this fall in W result in a reduction in the demand for capital, K?  Explain your answer.

3.  The negative income tax has never been adopted on a national basis, but it has been implemented in a number of experiments in various localities.  In each of these experiments, families were chosen at random and were given cash payments – small amounts for families close to the "breakeven" or poverty-line level of income; greater amounts for families with much less income. (Families above breakeven received no payment.)  Professor Howard M. Wachtel, in his textbook, Labor and the Economy (New York:  Academic Press, 1984, p. 63), commented that as a result of the negative income tax, a "pure income effect [was] introduced into the household's decision about how much labor to supply to the market." Do you agree with this description of the impact of the negative income tax?  If so, explain why.  If not, explain why not.

4.  A firm produces output Q using inputs of labor (E) and capital (K), with prices W and R, respectively.  Production is subject to an upward-sloping marginal cost curve.  Now suppose W rises. Discuss each of the statements below, explaining whether it is correct or incorrect and why:

A.         "If output (Q) rises after the increase in W, then we can be sure that K is a normal input."

B.         "If K is a normal input, then we can be sure that output (Q) will rise due to the increase in W."

5. Jim earns a wage W of $20/hour, and receives $100/month in nonwork income V by renting an apartment that he owns. Then the apartment burns down, so his nonwork income falls to zero – but he simultaneously gets a raise that bumps his wage from $20 to $30 per hour.  Both before and after these events, he is in equilibrium.  This is summarized in the following table:

                                             before          after

Jim adds, "I still have exactly the same amount of utility now as I did before the changes in W and V."

A.         Given this information, is it possible to say whether Jim now consumes more consumption goods C than he did before these changes in W and V?  Why, or why not?  Explain your answer.

B.         Given this information, is it possible to say whether Jim now consumes more leisure time L than he did before these changes in W and V? Why, or why not?  Explain your answer.

6.  Edgar Economist has performed a regression analysis of the annual hours of work H of a large number of single women who receive welfare benefits, and has obtained the following results:

H = 451.02 + 12.91 W – 0.21 B + e

(22.01)  (4.09)   (0.03)

where W = hourly wage; B = amount (in dollars) of welfare benefits received per year; and e = omitted variables. The figures in parentheses are the standard errors of the coefficients appearing immediately above them.  (None of these women receive any "nonwork" income (V) such as interest, dividends, or rental income.)

A.        "Aha!" says Congressman Ranton, "Edgar's results show that paying welfare benefits reduces hours of work!"  If we ignore the possibility of missing-variables bias, is Ranton's claim correct? Explain why or why not.

B.         Eve Econometrician comments, "Edgar's results may be affected by missing-variables bias, and may therefore exaggerate the negative effect of welfare benefits B on hours of work H."  Under what conditions could Eve be correct? (Ignore the possibility that the coefficient on W could be affected by missing-variables bias.)

KEY TO THE MIDTERM EXAM

1.  Note that since W rises from 20 to 30, and since P rises from 10 to 15, the real wage hasn't changed: W/P = 20/10 = 30/15 = 2.  So there will be no change in the slope of Jane's budget line, and there will therefore be no substitution effect of these changes.  However, although P has changed, V ( = nonwork income) has not! And since V/P falls (from 14/10 to 14/15), we know that her real nonwork income has fallen.  (In other words, the purchasing power of her dollars of nonwork income has fallen.) So this will have a pure income effect on her behavior, and will make her worse off.  You're told that leisure, L, is a normal good.  Since she is now worse off, she will reduce L.

Eight points for noting that (and explaining why) the change in W/P won't change the slope of Jane's budget line, and will therefore have no substitution effect.  Another eight points for noting that (and explaining why) the change in V/P will shift Jane's budget line down and will have a pure income effect on behavior.  Eight or nine points for noting that since L is a normal good, this change will reduce leisure time, L.

2.  This kind of question is best answered by first working through the substitution effect and the possible scale effects, and then applying them to the case at hand.  (See, e.g., Question 4 below.)

If W falls, the substitution effect will reduce K and increases E. The effect on MC, Q and the scale effect on each input will depend on whether E is a normal input.

If E is a normal input, the fall in W will reduce MC.  In turn, the drop in MC will raise profit- maximizing Q.  Since E is normal, the scale effect on E will be positive, i.e., E will rise.  If K is normal, demand for K will also rise; but if K is regressive, K will decrease.

If E is a regressive input, the fall in W will raise MC.  In turn, the increase in MC will reduce profit-maximizing Q.  Since E is regressive, the scale effect on E will be positive; E will rise. If E is regressive, then K must be normal (both inputs can't be inferior!), and since Q falls, K will fall as well.

5 points for an answer like this (though not necessarily identical to this) that lays out the various possible responses to a rise in W. With this, we can now answer both parts of the question:

A.  A decrease in W will always increase demand for E, regardless of whether E is normal or regressive; as shown above, when the wage falls, the substitution effect always raises E, and regardless of whether E is normal or regressive, the scale effect also raises demand for E. (Thus, the substitution and scale effects of a wage change always work in the same direction.) 10 points for a good answer along these lines.

B.  A decrease in W always reduces demand for K via the substitution effect.  But the scale effect on demand for K of a decrease in W is "iffy":

* If E is a normal input, then the scale effect on K will be positive if K is normal, but it will be negative if K is regressive.  Thus, we can be sure that K will fall (i.e., we can be sure that the sum of the substitution and scale effects on K will be negative) only if K is regressive.  In contrast, if K is normal, then the net effect on K of a decrease in W depends on whether the negative substitution effect on K is stronger or weaker than the positive scale effect.  Five points for a good answer here.

* If E is a regressive input, then K must be a normal input.  Here, the substitution effect of a wage decrease on K will be negative, and since MC rises, Q will fall, and so K will fall as well.  Five points for a good answer here.

3.  Professor Wachtel is mistaken.  Remember that the negative income tax (NIT) has two effects. First, an NIT does indeed give money to families below the poverty line.  This would certainly

generate an income effect; and, leisure is a normal good, it would make it possible (and would encourage!) families to supply less labor and enjoy more leisure.  However, an NIT also has another effect: it reduces the wage by "taxing" earnings (more precisely, the net wage is now lower because whenever the household earns another dollar, some of that dollar will be "taxed away" in the form of benefit reductions).  Put more simply, as the question reminded you, the NIT gives "small amounts for families close to the 'breakeven' or poverty-line level of income [, and] greater amounts for families with much less income."  This reduction in the net wage (like any reduction in the wage) will have not only an income effect, but also a substitution effect.  So Prof. Wachtel is incorrect in saying that the NIT has only an income effect (or, in his words, that the NIT has a "pure" income effect): it will have an income effect because it makes people better off, but it will also reduce the wage, which will have both an income effect and a substitution effect.

10 points for noting that the NIT gives people money and, therefore, does have an income effect (so Wachtel isn't totally wrong).  However, another 15 points if (and only if) you noted that this isn't the whole story:  the NIT also reduces the wage because it "taxes" earnings, and this will have both an income effect and a substitution effect.

Since the NIT reduces the net wage, the substitution effect will therefore reduce hours of work and increase hours of leisure. The income effect coming from giving people more money will also reduce hours of work and increase hours of leisure (provided leisure is a normal good).  Finally, the income effect of the NIT's reduction in the net wage would tend to increase hours of work and reduce hours of leisure, but this effect is swamped by the fact that, on balance, NIT recipients do end up getting more income (despite the "taxation" of earnings and reduction in the net wage). So, provided leisure is a normal good, the NIT's income effect will reduce work and increase leisure (on balance) via an income effect, but it will also have a substitution effect that will also reduce work and increase leisure.

4.  This kind of question is best answered by first working through the substitution effect and the possible scale effects, and then applying them to the case at hand.  (See, e.g., Question 2 above.)

If W rises, the substitution effect will reduce E and increase K. The effect on MC, Q and the scale effect on each input will depend on whether E is a normal input.

If E is a normal input, the rise in W will raise MC.  In turn, the rise in MC will reduce profit- maximizing Q.  Since E is normal, the scale effect on E will be negative, i.e., E will fall.  If K is normal, demand for K will also fall; but if K is regressive, K will increase.

If E is a regressive input, the rise in W will reduce MC. In turn, the reduction in MC will raise profit-maximizing Q.  Since E is regressive, the scale effect on E will be negative; E will fall.  If E is regressive, then K must be normal (both inputs can't be inferior!), and since Q rises, K will rise as well.

5 points for an answer like this (though not necessarily identical to this) that lays out the various possible responses to a rise in W. So we can now consider both parts of the question:

A.  The statement is correct.  If Q rises after the increase in W, that must mean that E is regressive, and, in turn, that must mean that K is normal.  10 points for a good answer along these lines that draws on the above analysis of substitution and scale effects.

B.  The statement is incorrect (or correct only some of the time).  If K is a normal input, then, logically, E could either be a normal input or a regressive input. If E is regressive, then a rise in W will reduce MC, and in turn that will indeed result in an increase in Q. However, if E is normal, then a rise in W will raise MC, and in that case Q fill fall.  10 points for a good answer along these lines that draws on the above analysis of substitution and scale effects.

5.  Note that since Jim has exactly the same level of utility both before and after these changes in W and V, he must be moving around on the same indifference cure.  Before the wage changes, he has a wage of $20 per hour; after the wage changes, he has a wage of $30 per hour but with the same level of utility.

A.         Given this information, we can be sure that Jim's budget line has remained tangent to the same indifference curve (remember that utility is unchanged), but the wage is higher than it was before. Thus, he must have moved in a northwesterly direction along the indifference curve.  C must be higher. 10 points for a good answer along these lines.

B.         For just the same reason, since Jim's budget line has remained tangent to the same indifference curve and he has moved in a northwesterly direction along the same indifference curve, L must be lower. In fact, this is a pure substitution effect! (Utility stayed the same, but the wage went up.)  10 points for a good answer along these lines.

Finally, five points for saying (somewhere in your answer) that the key to understanding this is that utility has remained the same, so that we're just looking at the substitution effect of a higher wage.

6.  The key to answering this question is to note that welfare benefits B depend on earnings.  In particular, the more you earn, the smaller your welfare benefits B will be.  Next, note that the error term e here refers to missing variables (variables not explicitly included in the analysis) that positively affect H, hours of work.  Any time e rises, H must rise.  If “laziness” is among the missing variables, all that is necessary to fit it into this framework is to recast it as its opposite, “negative laziness” or “capacity for hard work.”  An increase in e then means hard(er) work; a decrease in e then means more laziness.  Since missing variables e positively affects hours of work H, and since B falls whenever H rises, it follows that e and B must be negatively correlated!  Five points for noting this.

A.  If we ignore the possibility of missing-variables bias, then Congressman Ranton is entirely correct. The coefficient on B in the regression is -0.21, which means that, other things being equal, an increase in B will reduce H. Moreover, this coefficient is clearly statistically significant: the t-statistic for this coefficient is 0.21/0.03 = 7.00, which is well above the threshold of 1.96 which is required for statistical significance at conventional test levels.  Eight points for noting the meaning of the coefficient on B (including both the meaning of the coefficient’s negative sign and the coefficient’s statistical significance).

B.  Eve Econometrician is quite likely to be correct.  Note from the above that e and B must almost certainly be negatively correlated. Whenever an included variable (like B) is negatively correlated with the error term, the estimated coefficient on the included variable will be downward-biased – either less positive than the true coefficient (if the true coefficient is positive itself), or more negative than the true coefficient (if the true coefficient is negative). In this case, it seems likely that the true coefficient on B is negative (i.e., benefits B do indeed reduce hours of work), but the problem with this estimate, -0.21, is that it may well be downward-biased, or in other words “too negative”  -- it will overstate the extent to which B actually does reduce H.  12 points for a good answer along these lines, noting that it’s likely that B and e are negatively correlated (as argued above) and that, therefore, the estimated coefficient on B will be “too negative,” i.e., downward-biased relative to the true coefficient.