The Rossett Ruby Company has a monopoly on the supply of rubies. At its current level of output the marginal cost of producing rubies is $1000 per carat. If the firm maximizes profit it will set the price of rubies at:

When interest is compounded continuously, the amount of money increases at a rate proportional to the amount s present at time t, that is, ds/dt = rs, where r is the annual rate of interest. (a) find the amount of money accrued at the end of 3 years when $4000 is deposited in a savings account drawing 5 3 4 % annual interest compounded continuously. (round your answer to the nearest cent.) $ (b) in how many years will the initial sum deposited have doubled? (round your answer to the nearest year.) years (c) use a calculator to compare the amount obtained in part (a) with the amount s = 4000 1 + 1 4 (0.0575) 3(4) that is accrued when interest is compounded quarterly. (round your answer to the nearest cent.) s = $

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.

For each separate case below, follow the 3-step process for adjusting the prepaid asset account at december 31. step 1: determine what the current account balance equals. step 2: determine what the current account balance should equal. step 3: record the december 31 adjusting entry to get from step 1 to step 2. assume no other adjusting entries are made during the year. a. prepaid insurance. the prepaid insurance account has a $4,700 debit balance to start the year. a re- view of insurance policies and payments shows that $900 of unexpired insurance remains at year-end. b. prepaid insurance. the prepaid insurance account has a $5,890 debit balance at the start of the year. a review of insurance policies and payments shows $1,040 of insurance has expired by year-end. c.prepaidrent.onseptember1ofthecurrentyear,thecompanyprepaid$24,000 for 2 years of rentfor facilities being occupied that day. the company debited prepaid rent and credited cash for $24,000.