EconS 404, Professor Rosenman
Week 3 Answers
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?)
Since the time constraint is binding, much of their income is not spent, thus they
can save a lot.
Question. Which program leaves the worker is better off?
It depends on the person's preferences (where their highest indifference curve is
tangent to the different budget constraints). If they "like" dependent
care, the indifference curve would be skewed towards the dependent care axis, and it would
be tangent to the dotted line. If they like other goods more, and use very little
dependent care, they might be better off with the lighter budget constraint that comes
with the tax credit.
Question. Who needs the review lesson in economics?
The graph shows the real story. Let X represent electricity and Y represent all other goods, with the price of Y normalized to equal one. Suppose the increase in the price of electricity is in the form of a per unit tax, T. The resulting increase from Px to Px+T, will pivot the budget constraint to line b. Assuming the individual demand for electricity is downward sloping, the amount consumed will fall from X1 to X2 because of the higher price. Tax collections can be read directly off the vertical axis as the distance between consumption on the original budget constraint, line a, and the new one, line b at the new level of consumption. If this sum is returned to this consumer, it is an income increase causing a parallel shift to line c.
Is the consumer as well off? Obviously not. Before the tax on electricity he
achieved a utility level of U1. On the new budget constraint, line b, he can no
longer afford that level of utility. A careful analysis of the problem indicates that
since the substitution effect will move consumption away from electricity, the income
effect cannot be totally offset by returning tax collections to the consumers. The budget
constraint has been tampered with in such a way that overall utility will be lower.
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. 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.
So we maximize the function L = X½+Y½ -l(200-X-2Y)
Taking the derivatives of L with respect to X and Y give the following expressions:
½X-½ + l =0 and ½Y-½ + l2 =0 which can be transformed to
½X-½ = - l and ½Y-½ = - l2. We need to solve for X and Y using these expressions and the budget constraint, 200=X+2Y. So divide ½Y-½ = - l2 by ½X-½ = - l , which gives
X½/Y½ =2. Square both sides and we end up
with X/Y=4 or X=4Y. Thus, 200=6Y or Y=200/6=33.333 and X=133.32