A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and corporate bond fund, and the third is a T-bill money market fund that yields a sure rate of 5.5%. The probability distributions of the risky funds are: Expected Return Standard Deviation Stock fund (S) 15% 32% Bond fund (B) 9% 23% The correlation between the fund returns is 0.15. a. What would be the investment proportions of your portfolio if you were limited to only the stock and bond funds and the portfolio has to yield an expected return of 12%? b. Calculate the standard deviation of the portfolio which yields an expected return of 12%.

Suppose a firm faces a fixed price of output, 푝푝= 1200. the firm hires workers from a union at a daily wage, 푤푤, to produce output according to the production function 푞푞= 2퐸퐸12. there are 225 workers in the union. any union worker who does not work for this firm is guaranteed to find nonunion employment at a wage of $96 per day. a. what is the firm’s labor demand function? b. if the firm is allowed to choose 푤푤, but then the union decides how many workers to provide (up to 225) at that wage, what wage will the firm set? how many workers will the union provide? what is the firm’s output and profit? what is the total income of the 225 union workers? c. now suppose that the union sets the wage, but the firm decides how many workers to hire at that wage (up to 225). what wage will the union set to maximize the total income of all 225 workers? how many workers will the firm hire? what is the firm’s output and profit? what is the total income of the 225 union workers? [hint: to maximize total income of union, take the first order condition with respect to w and set equal to 0.]

True or flase? a. new technological developments can us adapt to depleting sources of natural resources. b. research and development funds from the government to private industry never pay off for the country as a whole; they only increase the profits of rich corporations. c. in order for fledgling industries in poor nations to thrive, they must receive protection from foreign trade. d. countries with few natural resources will always be poor. e. as long as real gdp (gross domestic product) grows at a slower rate than the population, per capita real gdp increases.

Kyle and alyssa paid $1,000 and $4,000 in qualifying expenses for their two daughters jane and jill, respectively, to attend the university of california. jane is a sophomore and jill is a freshman. kyle and alyssa's agi is $135,000 and they file a joint return. what is their allowable american opportunity tax credit after the credit phase-out based on agi is taken into account?