You invest $100 in a risky asset with an expected rate of return of 0.11 and a standard deviation of 0.20 and a t-bill with a rate of return of 0.03. what percentages of your money must be invested in the risky asset and the risk-free asset, respectively, to form a portfolio with an expected return of 0.08?

5. profit maximization and shutting down in the short run suppose that the market for polos is a competitive market. the following graph shows the daily cost curves of a firm operating in this market. 0 2 4 6 8 10 12 14 16 18 20 50 45 40 35 30 25 20 15 10 5 0 price (dollars per polo) quantity (thousands of polos) mc atc avc for each price in the following table, calculate the firm's optimal quantity of units to produce, and determine the profit or loss if it produces at that quantity, using the data from the previous graph to identify its total variable cost. assume that if the firm is indifferent between producing and shutting down, it will produce. (hint: you can select the purple points [diamond symbols] on the previous graph to see precise information on average variable cost.) price quantity total revenue fixed cost variable cost profit (dollars per polo) (polos) (dollars) (dollars) (dollars) (dollars) 12.50 135,000 27.50 135,000 45.00 135,000 if the firm shuts down, it must incur its fixed costs (fc) in the short run. in this case, the firm's fixed cost is $135,000 per day. in other words, if it shuts down, the firm would suffer losses of $135,000 per day until its fixed costs end (such as the expiration of a building lease). this firm's shutdown price—that is, the price below which it is optimal for the firm to shut down—is per polo.

On coral island in 2012, the labor force is 12,000, the unemployment rate is 10 percent, and the labor force participation rate is 60 percent. during 2013, 200 unemployed people found jobs and the working-age population increased by 1,000. the total number of people in the labor force did not change. the working-age population at the end of 2013 was the unemployment rate at the end of 2013 was round up to the second decimal. the labor force participation rate at the end of 2013 was round up to the second decimal.

In each of the following, what happens to the unemployment rate? does the unemployment rate give an accurate impression of what’s happening in the labor market? a.esther lost her job and begins looking for a new one.b.sam, a steelworker who has been out of work since his mill closed last year, becomes discouraged and gives up looking for work.c.dan, the sole earner in his family of 5, just lost his $90,000 job as a research scientist. immediately, he takes a part-time job at starbucks until he can find another job in his field.