Suppose you are offered $100 now or $125 in 5 years. Let the interest rate be 4 percent. Calculate the present value of the $125 option. Which option should you take if your goal is to choose the option with the larger present value?
2. Becky works in sales but is considering quitting work for 2 years to earn an MBA. Her current job pays $40,000 per year (after taxes), but she could earn $55,000 per year (after taxes) if she had a master’s degree in business administration. Tuition is $10,000 per year, and the cost of an apartment near campus is equal to the $10,000 per year that she is currently paying. Becky’s discount rate is 6 percent per year. She just turned 48 and plans to retire when she turns 60, whether or not she gets her MBA. Based on this information, should she go to school to earn her MBA? Explain carefully.
3. If Ann stops going to school after she gets a high school diploma, the present value of her lifetime earnings will be $500,000. If she obtains a college education, the present value of her lifetime earnings will be $800,000. If Sarah stops going to school after she gets a high school diploma, the present value of her lifetime earnings will be $500,000. If she obtains a college education, the present value of her lifetime earnings will be $600,000.
a. What is the percent increase in earnings that Anne faces if she gets a college education (i.e. her gross rate of return)? What is Sarah’s gross rate of return to a college education? What is the average gross rate of return to college in this two--person economy?
b. The present value of the cost of college is $110,000 for both women. Given this information, what education decision will each woman make? Based on those decisions, what will be the magnitude of the rate of return to education estimated by the researcher who observes these two data points?
c. Explain the term “selection bias” in the context of this example.
4. Suppose that Hal (a high productivity worker) and Lou (a low productivity worker) are deciding whether or not to complete a four--year college degree. Even though Hal and Lou are thinking of attending the same college, Lou has higher “emotional costs” associated with each year attended. Suppose that Hal’s cost of college attendance is given by:
CHAL(s) = $20,000*S (S = years of schooling) And Lou’s cost of attendance is given by:
CLOU(s) = $30,000*S
a. Suppose a firm offers all college graduates earnings equal to $300,000 (in present value) and all high school graduates earnings equal to $200,000 (in present value). Will Hal choose to go to college? Will Lou choose to go to college? Is this a pooling or a separating equilibrium?
b. Suppose the firm now offers high school graduates earnings equal to $150,000 (in present value). Does this affect Hal’s schooling decision? Does this affect Lou’s schooling decision? Is this a pooling or a separating equilibrium?
c. Assuming that the firm continues to offer $300,000 (in present value) to college graduates, what range of wages for high school graduates will generate a separating equilibrium?
d. What are two key assumptions that differentiate the signaling model from the human capital model?
5. Consider an economy with the following income distribution: Each person below the 25th percentile of the income distribution earns $15,000. Each person between the 25th and 50th percentiles earns $30,000. Each person between the 50th and 75th income percentiles earns $45,000. And each person between the 75th and 100th percentiles earns $60,000.
a. Graph the Lorenz Curve and calculate the Gini Coefficient for this economy.
b. Now suppose the bottom quartile pays no taxes, the 2nd quartile (25--50th) pays 10% in taxes, the 3rd quartile (50th--75th) pays 20% in taxes, and the top quartile (75th to 100th) pays 30%. Two thirds of all tax money collected is redistributed equally to all citizens in the form of military defense, government pensions, roads/highways and so on, and the other one third is distributed evenly only among the poorest quartile of citizens. Draw the new Lorenz Curve and calculate the new Gini Coefficient.
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