Wednesday, February 20, 2013

Indifference curve and budget line applications

1. Suppose you spend some of your income on compact disks (CD) and the rest  of your income (Ig) on other goods.
a. Depict an initial optimum in an indifference curve diagram. Put CD on  the horizontal axis. Use an "a" to label your initial consumption  bundle.
b. Now suppose that you have the opportunity to join a CD buying club in  which you can purchase CDs at half their regular price. As an  introductory offer, there is no membership fee. In your diagram depict  your new equilibrium if you join the CD buying club.
c. Clearly separate your change in total CD purchases into a substitution  effect and an income effect.
d. Now suppose instead that you wait too long to join, and the buying  club adopts the maximum membership fee at which you would consider  joining the club. Indicate the size of this fee in your diagram.
e. Finally, suppose the membership fee is instead set just high enough to  allow you to continue to consume the bundle labelled "a" in your  diagram. Indicate the size of the membership fee in this case. Would  you join the CD buying club under these circumstances or not? If not,  explain why not. If so, explain why, and illustrate a possible new optimum.

2. Consider a consumer who purchases health care (H) and spends the rest of her money income (Ig) on other goods.
a. Use an indifference curve diagram to depict an initial situation in which the consumer's health care costs are subsidized by her employer.
b. Suppose the consumer's employer unilaterally cancels the health care subsidy. Depict the consumer's new optimum in your diagram.
c. Suppose now that the employer raises raises her money income just enough to restore the welfare level she enjoyed with the health plan. Use your diagram to indicate the size of the income increase.
d. If the employee's money income plus any health care costs absorbed by the firm constitute the firm's total cost for this employee, will this total cost be higher or lower now than it was under the health plan? Explain briefly, and use your diagram to support your answer.
e. Will this employee consume more or less health care under this arrangement compared to the health plan of part a? Explain briefly.

3. Consider a family which consumes housing (H, measured in square feet) and  spends the rest of its income (Ig) on other goods).
a. Depict an initial optimum for this family in an indifference curve  diagram. Suppose now that the government decides to subsidize housing  costs for this family. Depict the consequences of this policy in your diagram. Use H* to label the quantity of housing purchased under the subsidy policy.
b. Indicate in your diagram the cost of this policy to the government.
c. Now consider again the pre-policy situation in which this family experiences utility level Uo. Indicate in the diagram the maximum total housing expenditure which this family would be willing to make to move into a public housing project (i.e., government-constructed housing) which gives the family exactly H* units of housing.(Hint: How much income could the family give up to consume H* without a reduction in its utility?)
d. Suppose that the government can purchase or construct public housing at the going market price, and that the goal of public policy is to encourage this family to purchase H* units of housing but not necessarily to raise the family's level of utility. If the government could actually collect from the family the amount you indicated in part c, which policy would be less costly for the government, the housing subsidy option or the public housing option? Use your diagram to carefully support your answer.

 4. Consider two families, Poor (p) and Rich (r), each with one child and each with the same set of preferences regarding its child's education. However, family r has a higher income than family p. The diagram to the right reflects the situation both families would face by purchasing education (E) for their children using private school systems and spending the rest of their money income (Ig) on other goods. a. Do these families consider education to be a normal or an inferior good? How can you tell? b. Now suppose that both families have the option of choosing a public education or a private school for their children. The families can use the public education system at no charge, and any child sent to a public school receives 2 "units" of education. Indicate in the diagram the consumption bundle each family will achieve if it elects the public school option. Also add indifference curves to illustrate the welfare change each family will experience if it chooses the public school option. c. Will family p choose the public school option? What about family r? Briefly explain both answers.
 5. Economist David Friedman demonstrated that people who already own a home can end up better off when housing prices either rise  or  fall. Use indifference curves to show that Friedman is correct, and also show that, for a  potential  homeowner, "it pays to buy now if you expect housing prices to rise in the future and pays to wait if you expect them to fall." In other words, demonstrate that (1) if housing prices rise, homeowners will end up better off than they would have been if they had waited to buy their first house until after the price increase; (2) if housing prices fall, homeowners will end up worse off than they would have been if they had waited to buy their first house until after the price decline. Use separate diagrams to illustrate a price increase and price decrease, put square feet of housing (H) on the horizontal axis and income spent on other goods (Ig) on the vertical axis.