Dr. ruth is going to borrow $8,400 to write a book. the loan is for one year and the money can either be borrowed at the prime rate or the libor rate. assume the prime rate is 8 percent and libor 1.3 percent less. also assume there will be a $48 transaction fee with libor (this amount must be added to the interest cost with libor).

a.
what is the effective interest rate on the libor loan?

Mr. smith recently faced a choice between being (a) an economics profes-sor, which pays $60,000/yr, or (b) a safari leader, which pays $50,000/yr. after careful deliberation, smith took the safari job, but it was a close call. "for a dollar more," he said, "i'd have gone the other way."now smith's brother-in-law approaches him with a business proposition. the terms are as follows: - smith must resign his safari job to work full-time in his brother-in-law's business.- smith must give his brother-in-law an interest-free loan of $100,000, which will be repaid in full if and when smith leaves the business. (smith currently has much more than $100,000 in the the business will pay smith a salary of $70,000/yr. he will receive no other payment from the business.the interest rate is 10 percent per year. apart from salary considerations, smith feels that working in the business would be just as enjoyable as being an economics professor. for simplicity, assume there is no uncertainty regarding either smith's salary in the proposed business or the security of his monetary investment in it. should smith join his brother-in-law and, if so, how small would smith's salary from the business have to be to make it not worthwhile for him to join? if not, how large would smith's salary from the business have to be to make it worthwhile for him to join?

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.

Alarge tank is filled to capacity with 500 gallons of pure water. brine containing 2 pounds of salt per gallon is pumped into the tank at a rate of 5 gal/min. the well-mixed solution is pumped out at the same rate. find the number a(t) of pounds of salt in the tank at time t.