Labor, Consumer Behavior, and Income Distribution

Consumer Behavior

CB-1. A consumer buys two goods, X and Y, and has known money income I per time period. Show the consumer's effective budget constraint in each of the following cases. [A carefully labeled graph will probably be sufficient in each case. If you give the equation for the constraint, be sure to graph it as well.]

  1. The consumer can buy X and Y at known, fixed prices px and py.
  2. The consumer pays a fixed price for good X, say $1 per unit. Good Y costs $1 per unit for the first 10 units bought, and $.50 per unit for units bought in excess of 10. ( [Assume I > $10.]
  3. The consumer with income I is given 10 units of good X which cannot be sold to another consumer. Show the effect on the effective budget constraint of the gift.
  4. The consumer must pay a tax of 1pxon all units of X consumed.
  5. Consumption of X and Y require time as well as money. The fixed money prices of the goods are px and py Consumption of X requires 1 hour per unit consumed, and Y requires 2 hours per unit consumed.

CB-2 John's utility from the consumption of steak and beans is given by:

U = S.5 B.3

where U is his total utility, and S and B are the amounts of steak and beans consumed per week. In each week John has a money income of I and the prices of steak and beans are constant. (John has no market power.) John maximizes his total utility.

a. Find the price elasticity of demand for steak.

b. Find the income elasticity of demand for steak.

c. Find the cross-price elasticity of demand for steak with respect to changes in the price of beans.

CB-3 Short questions (do any 3):

a) Consider the utility function U = X2Y. Find and graph the marginal rate of substitution MRSxy at X = 2 and Y = 9.

b) Consider the utility function U = min(X,3Y). Let Px=2 and PY = 1 Find and graph the Engel curve for Y and use it to find Y* if I = 168 (I = income)

c) Bill has utility function U = min(2X,Y). Using Px = 2, Py = 3, and I = 88, find Bill's demand curve for X.

d) Sara' s utility function is U = X2Y. Originally, Px=2. Py=5 and I = 300. If Py increased to 10, how much would Sara have to be compensated to return her utility to the original level?

CB-4 Supposea consumerhasthefollowingpreferencesovertwogoods,foodandclothing,

U(f,c)= f 1/2c1/2

andfacespricespfandpC,withincomeI.

A.DerivetheMarshalliandemandsfortheconsumer.

B.Derivetheconsumer'sindirectutilityfunctionandprovidea briefexplanationofitsmeaningand significance.

C.Derivetheconsumer'sexpenditurefunctionandprovidea briefexplanationofitsmeaningand significance.

D.Inthe1960's,whenthecalculationofthepovertylinewasintroducedintheUS,theaveragefamily spenta thirdofitsincomeonfood. Hencethepovertylinewasestablishedbymultiplyinga "minimallysufficientfoodbudget"bya factorof3 andcallingthatlevelofincomethepoverty line. Inthe1990'stheshareofincomespentonfoodisabout1/8.Isa Cobb-Douglasutilityfunction,like theoneabove,wherethetwogoodsarefoodandallotherconsumption,consistentwiththese observations?Proveyouranswer.

CB-5. Consider a consumer with income, M, and the following utility function defined over two goods, x1 and x2 with prices p1 and p2:

U = x11/3 x22/3

(a)Derive the demand for x1.

(b)Determine if the two goods are substitutes or complements.

(c)Calculate the elasticity of substitution between the two goods. How do the shares depend on the parameters of the problem.

(d)Calculate the expenditure shares on the two goods. How do the shares depend on the parameters of the problem

CB-6. You allocate your entire income between Peanut Barrel cheeseburgers and mugs of an amber colored beverage served by the local brewpub. At your current consumption levels, MUCheeseburger= 3 and MUBeverage= 4. Prices for the two goods are PCheeseburger = $1.50 and PBeverage = $3.00.

a)Explain why your current consumption bundle does not maximize your utility.

b)B.Would your utility maximizing “bundle” include more or less of the amber colored beverage? Explain.

Labor Supply

LS-1. The US Congress has recently increased marginal tax rates for taxpayers with high incomes. Martin Feldstein and others have argued that labor supply responses (and other behavioral responses) by high income taxpayers may drastically reduce the revenue that these tax increases bring in.

  1. Standard theory says that for a flat-rate (proportional) tax, the direction of the labor supply response to an increase in the rate is indeterminate (work effort might increase, decrease, or remain the same.) Explain. (A graph may help.)
  2. For concreteness, consider the following hypothetical example. An individual earns $120,000 and pays a 30% tax on all of that income. In which case would you expect him to reduce his labor supply more: 1) the tax on all income is increased to 40%, or ii) income up to $1000,000 is still taxed at 30%, but any additional income is taxed at a 40% marginal rate? Explain.

LS-2. There are only two types of jobs, paying annual wages w1 and w2, which remain constant over time. All workers have equal abilities and working conditions are equivalent across jobs, but job 2 requires one extra year of training. The only cost of the training is that you cannot work for pay during that time. The interest rates is r. Workers have infinite time horizons. In competitive equilibrium, what is the relationship between w1 and w2?

LS-3. The 1981 reductions in the personal tax rates were put through with the expectation that they would increase willingness to work and to save. Some of the more optimistic projections claimed that the outpouring of effort would be so big that government revenue would actually increase.

  1. How large would labor supply elasticities have to be in order for government revenue to rise with a reduction in the tax rate. Explain your calculation.
  2. Theoretically, what is the sign of labor supply elasticities? Explain.
  3. Labor supply elasticities for women, the old, and the young are measured to be considerably larger than for men. Explain the likely explanation for this observation.

Labor Demand

LD-1. Two factors of production are said to be complementary if increased employment of one raises the marginal product of the other.

  1. Give an example of complementary factors and explain.
  2. For profit maximizing firms, provide the optimal factor employment conditions for two factors that would hold whether or not the firm is a price-taker in the product market and whether or not the firm is a price-taking employer. (Assume the supply of factors is competitive.) Explain.
  3. What is the relationship between marginal factor cost and the price of a factor for a monopsonist? Explain why it is so.
  4. If two factors are complementary, will the demand curve for either be the same as its marginal revenue product curve? Explain why or why not and derive the demand curve. What if the two factors are anti-complementary (increased employment of one lowers the marginal product of the other?) Again explain why or why not and derive the demand curve.

LD-2. Answer the following as true, false, or uncertain. Explain carefully. Your credit depends entirely on your explanation.

  1. If the wage rate for skilled workers is twice the wage for unskilled workers, then a cost-minimizing firm will use fewer skilled than unskilled workers to produce any given output.
  2. The auto workers should receive a substantial pay raise because such a raise will induce the auto manufactures to find more efficient methods of production and will therefore, cause a fall in the average price of automobiles in the long run.

LD-3. Jacqueline Jones of Brandeis University, is quoted in the New York Times as finding a parallel between the mechanization of 19th century agriculture that caused social displacement and economic upheavals around the time of the Civil War and the mechanization of the 20th century office, reducing job security and causing downward economic mobility for large segments of the current U.S. middle class. Just as poverty and underemployment of displaced cotton farmers in the 19th century could be traced to forces beyond their control, so to she argues that the economic fortunes of the great mass of American white collar workers is beyond their individual control as well. She says, "Americans must come to grips with the fact that unemployment is not a reflection of one's character. It is pegged to international transformations. . . Being in the right place at the right time--namely, in an expecting sector of the economy--is more important than being hard working." Using the standard models of labor economics

  1. Trace through the effects of a technological change like computerization of the workplace on wages and/or employment.
  2. Trace through the effects of a decrease in demand for the products of the industry that one is employed in on the wages and/or employment in an industry.
  3. In the standard model of wage determination without human capital considerations, explain the extent to which one's own productivity (as opposed to that of one's co-workers or those outside the industry) affects one's wages and/or employment.
  4. Explain how the introduction of human capital modifies your answer in part 3.

LD-4 Answer both of these short questions:

  1. Does the demand curve for labor slope downward for the same reason as the demand curve for goods and services?
  2. Which are usually thought to be larger: the elasticity of labor supply with respect to wages or the elasticity of labor demand with respect to wages? Explain briefly.

Labor Markets

LM-1. Some economists have alleged that the local market-for nurses' services can be correctly modeled as a monopsony in which there is only a single employer -- the local hospital.

  1. Explain how the wages of nurses and the level of employment are determined in this case.
  2. Is the level of employment efficient? Explain carefully.
  3. If the nurses form a union and bargain collectively over wages with the hospital, what are the implications for the level of wages and the employment level for nurses?

LM-2. A proposal to increase the minimum wage is now under consideration.

  1. Show how raising the minimum wage affects the number of unskilled workers employed and the total earnings of those with jobs. How are these affected by the elasticity of demand for unskilled labor?
  2. Explain what determines the elasticity of demand for unskilled labor in any given industry.
  3. Few, if any, union workers earn as little as the minimum wage, yet unions are among the loudest supporters of the proposed increase.
  4. Explain why unions think that high minimum wages are in their interest.
  5. Explain why few, if any union workers are paid the minimum wage.

LM-3. Business Week, in a recent issue, reported, "The great American job machine is fast becoming the eighth wonder of the world. While employment has declined in most industrial countries, the U.S. is creating jobs at breakneck speed. Many experts seem baffled by this phenomenon, but the reason is simple--women. Women have seized two-thirds of the jobs created in the past decade... But a new factor has suddenly emerged: Women are pushing harder than ever for equal pay and scoring some impressive gains." Women's wages bottomed at 57% of men's wages in 1973 and have risen to 64% in 1984. Business Week reports that, "Based on economics alone, women are on a path that conservatively will raise their wages to at least 74% of male wages by the year 2000." Explain what the article means when it says "based on economics alone." Sketch how one would go about forecasting future trends in women's wages.

LM-4. The most recent expansion in the U.S. business cycle started in 1992 and has gone on longer than economists had expected. In 1999, Allen Sinai, CEO of Primark Decision Economics said, “We’re in the midst of the greatest business expansion in U.S. history, and there is no end in sight.” One of the major surprises of this current expansion is that it has led to large increases in employment while not leading to substantial increases in wages paid to labor. Using standard microeconomic models of labor markets and the determinants of supply and demand for labor

1.1.Explain if can we infer from this that the demand for labor is highly elastic, that the supply of labor is highly elastic, or neither.

1.2.Describe the factors that determine the elasticity of supply and demand for labor.

1.3.Describe how we would decide if the demand for labor has changed since 1992 or if we are simply moving to a new point on the demand for labor curve.

1.4.Describe how we would decide if the supply of labor has changed since 1992 or if we are simply moving to a new point on the supply of labor curve.

Income distribution

ID-1. One reason that has been given to explain the increase in income inequality in the United States over the last approximately 15 years is that the rate of return to education has increased.

  1. What is meant by the rate of return to education? (You may provide a formula or explain verbally.)
  2. What is the economic explanation for why those with more education are pay a higher wage?

ID-2. The Reagan administration recently conceded that poverty has increased in the United States over the last four years. Especially apparent was the fact that the increase in poverty was not uniformly distributed across the population. Two parent families and families headed by blacks were especially hard hit. You are presumed not to have any information about what has happened in the country over the last four years. Instead you are asked to explain how you would go about investigating why this increase has occurred. Use your knowledge of the sources of income in the United States and the pattern of wages and labor force participation rates to explain where you would look for an explanation.
ID-3. Business Week several weeks ago had as its lead article the increasing income inequality in the United States and the detrimental effect that this inequality is having on the American economy. The Bureau of Labor Statistics says that according to some measures, the level of income disparity is the highest since they started keeping records.

  1. How is income inequality measured?
  2. Explain the standard difficulties and ambiguities involved in trying to assess the changes in the distribution of income over time or between countries.
  3. Make as complete a catalog as you can of the factors that economists have identified as important for determining the distribution of income
  4. Which of the factors to you believe have been most important for increasing the level of income disparity in this country? Explain your logic.

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