Analysis Problems
1. When the Federal Republic of Germany (West Germany) absorbed the German Democratic Republic (East Germany) in 1990, one of the most controversial issues was the rate of exchange that would be established between the currencies. Residents of East Germany had accumulated large amounts of savings, denominated in the East German currency, and were worried that their savings would lose value when converted to the West German mark.
Papers in the United States explored why East Germans, among the most prosperous inhabitants of the communist countries, saved so much. The indications were that time, rather than money, was the constraining factor in most consumption. Constant shortages and inefficiencies in providing goods forced the East Germans to wait in long lines in order to purchase most goods. And time spent waiting for meat was unavailable to use to wait for milk, bread or televisions. For most of the population, the consumption point was inside the monetary budget constraint, leaving unspent income which the East Germans saved.
Question. Draw 2 constraints on one indifference graph, one for money and one for time, with waiting in line the "price" of a good in terms of time. How does this show that residents of East Germany would save lots of their income? (HINT: Which constraint is binding on consumption?)
2. New Federal tax laws on dependent-care spending plans offer two alternatives for these benefit programs. The plans are intended to help workers plan for child care or care for other dependents while they are at work. Most plans offer two alternatives between which the worker must choose. One choice for the worker is to have wages set aside by his employer (up to 5000 dollars of pay in 1991). This set aside avoids taxes and is used by the employer to pay the worker's dependent care costs. Alternatively, the worker pays all costs with after-tax dollars, and then is eligible for a tax credit (in 1991 the credit was for expenses of up to 2400 dollars for one dependent, or 4800 dollars for two or more dependents receiving care). The credit rate is 30% of costs for taxpayers with incomes lower than 10000 dollars, and drops to 20% if income exceeds 28000 dollars.
Individuals see different impacts on their budget constraints depending on which alternative is chosen and what their income is. Consider a worker who earns 30000 dollars a year, pays an average income tax plus FICA tax rate of 17.5 percent, and must pay 3000 dollars per year in dependent care costs. Assuming the demand for dependent care is independent of price, that is the individual is forced to pay the 3000 dollars for the range of after tax costs under consideration, the two alternatives give different budget constraints.
Without any subsidy, taxes on 30000 dollars at a rate of 17.5 percent are 5250 dollars. The individual has 24750 dollars, of which 3000 dollars is spent on dependent care. Thus, 21750 dollars can be used to purchase other goods. The set-aside alternative allows the 3000 dollars to be paid with pre-tax dollars. As a result, only 27500 dollars goes to the worker as taxable income, so the tax is 4725 dollars. Since the 3000 dollars dependent care cost is already accounted for, 22275 dollars is available for purchasing other goods.
Alternatively, the worker can use the tax credit. In this case taxable pay is again 30000 dollars. After taxes but before dependent care 24750 dollars is available. All but 600 dollars of the 3000 dollars for dependent care is eligible for the 20 percent credit, which amounts to 480 dollars (20 percent of 2400). Thus, actual dependent care costs are 3000 dollars minus 480, or 2520 dollars. A total of 22230 dollars can be spent on other goods after dependent care costs are paid. The worker is worse off by 45 dollars.
Graphically, the two programs contrast the
effects of parallel shifts in a budget constraint, which illustrates an income change, and
a pivot in the constraint, which is indicative of a relative price change. In the graph
uses the heavy solid line to indicate the budget constraint without any subsidy program.
The after tax income of 24750 dollars is allocated between dependent care (at a price Pd)
and all other goods (price Pa). Point X indicates 3000 dollars worth of
dependent care.
The set-aside plan essentially avoids taxes on $3000 of income, moving the budget constraint to the heavy dotted line. Notice, it is parallel to the original line to the right of point X, where 3000 dollars is being spent on dependent care. The horizontal portion indicates that no change in the consumption in other goods is needed to increase dependent care up to 3000 dollars worth. All 22275 dollars of after tax pay is for other goods.
But if the tax credit is used (the light solid line), the price of dependent care falls to 80 percent of Pd for expenses up to 2400 dollars. Beyond that the price returns to Pd, thus the kink at an amount of dependent care equal to 2400/Pd. At 3000 dollars of dependent care expenses, only 22230 dollars is left to spend on other goods.
Question. Which program leaves the worker is better off?
3. The year 1990 was astonishing for the spread of the market based economic system to the previously planned economic systems in eastern Europe and the Soviet Union. Lindley H. Clark Jr., a columnist for the Wall Street Journal, reported on a study done by Robert Shiller of Yale University and two Soviet scholars, Maxim Boycko and Vladimir Korobov, which compared how well Russians and Americans understand markets (11/1/90). One question asked of those surveyed for the study "... supposed that the price of electricity was raised and consumers' incomes were raised exactly enough to cover the price increase. Would the consumer be better off, worse off, or would his situation be unchanged?" Most Soviets said that they would be unaffected, but Clark reported that "... an astonishing one-third of the Americans thought they would somehow be worse off," expressing incredulity that so many could be wrong. Is Clark correct in thinking so many Americans do not understand economics?
Question. Who needs the review lesson in economics? (HINT: Use an income-substitution effect analysis, and see what happens to the level of utility reached after the change.)
TECHNICAL PROBLEMS
1. In order to reduce crowding at the campus dining commons at lunch an economist suggested adding a "tax" on the food at peak hours. Each customer is then given enough extra cash so he or she could afford their original consumption. For example, suppose the normal price per unit of food = $1, and a person bought 3 units at peak hours, and 1 unit at nonpeak hours (a total of $4). If the peak price was raised to $2 per unit, the cost of the original consumption becomes $7, so this person received $3 as a subsidy.
a). Would this shift the use of the food service to different times?
b) Would the typical customer be better off, worse off or the same as before? Why?
2. A worker is offered two jobs. In the first she would work 30 hours a week at 4 dollars an hour. In the second she would work 20 hours a week at 5 dollars per hour. Everything about the jobs is the same except the for the hours and total salary. She claims to be indifferent between the two jobs. Could she be telling the truth? Explain.
3. A contrast in sales and income taxes come from the adjacent states of Washington and Idaho. Washington has no income tax, but does have a sales tax which applies to almost all consumer goods except food. Idaho has a smaller sales tax but applies it to all consumer goods including food, and a state income tax. Ignoring the work incentive effects of the income tax, how the different tax systems affect the consumption of food and all other goods.
4. (Calculus based
practice) Find the utility maximizing combination for X and Y if U=X½+Y½.
Use 200=X+2Y as the budget constraint. The derivative for a function Xa
is aXa-1 so the derivative of X½ is ½X-½.