Calculate the Marginal Utilities and Marginal Rate of Substitution for each of the Utility functions below. (Remember, marginal utility of a given good gives us the impact of an additional unit of that good on the total utility.)

Identifying transactions national park tours co. is a travel agency. the nine transactions recorded by national park tours during may 2019, its first month of operations, are indicated in the following t accounts: cash (1) 75,000 (2) 900 (7) 8,150 (3) 1,600 (4) 6,280 (6) 2,700 (9) 2,500 accounts receivable (5) 12,300 (7) 8,150 supplies (2) 900 (8) 660 equipment (3) 8,000 accounts payable (6) 2,700 (3) 6,400 beth worley, capital (1) 75,000 beth worley, drawing (9) 2,500 fees earned (5) 12,300 operating expenses (4) 6,280 (8) 660 indicate for each debit and each credit (a) whether an asset, liability, owner's equity, drawing, revenue, or expense account was affected and (b) whether the account was increased (+) or decreased account debited account credited transaction type effect type effect (1) (2) (3) (4) (5) (6) (7) (8) (9)

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.

You hold a diversified $100,000 portfolio consisting of 20 stocks with $5,000 invested in each. the portfolio's beta is 1.12. you plan to sell a stock with b = 0.90 and use the proceeds to buy a new stock with b = 1.50. what will the portfolio's new beta be? do not round your intermediate calculations.