.Solve the following questions

A firm uses two inputs, X and Y and its production function is Q = %(xy), where here we are using x and y to represent the quantities of the two inputs. (a) Calculate the marginal products of X and Y. (b) Does the firm's production function satisfy our three basic assumptions for production functions? (c) Does this production function have increasing, decreasing, or constant returns to scale? (d) Does this production function satisfy the Law of Diminishing Returns? (e) Draw the isoquant that shows the combinations of inputs that can produce Q=6. You should the exact coordintes of at least four points on the isoquant. Is this isoquant convex? (f) What is the firm's marginal rate of technical substitution of X for Y, at the point where it chooses x=9 and y=25? Assume that the demand for the firm's product is QD = 24 ! 4P, where P is measured in dollars. The firm has no control over the exogenous prices of its inputs, px>0 and py>0. The firm's problem is to choose x and y to maximize its profit. (g) Calculate the first-order condition for the firm's problem. (h) What are the boundary points of this problem? Under what conditions would the firm choose a boundary point? Be as specific as possible about which boundary point the firm would choose. (i) Assuming that the solution occurs at a point that satisfies the first-order condition, find four equations that determine the solution to the firm's problem. The four unknowns are x, y, Q, and P. For the rest of the problem, assume that px=$4 and py=$1. (j) Calculate the solution to the firm's problem. What are its profit-maximizing price and quantity of output? How much of each input does it use? What is the firm's maximum attainable profit? (k) At the firm's profit-maximizing level of output, calculate its average cost and marginal cost. (l) Draw the isocost line that shows the combinations of X and Y that have a total cost of $20. You should show the exact coordinates of the intercepts. Repeat this question, on the same diagram, for the isocost lines that imply a total cost of $12 and $32. (m) On the same diagram, show the firm's optimal point and the isoquant and isocost line that are tangent at that point. What is the firm's marginal rate of technical substitution of X for Y, at that point? (n) Suppose that the firm decides to produce Q=8. Its problem is to choose x and y to produce Q=8 at the lowest possible cost. Use the tangency condition (part of the first-order conditions) to solve this problem. Calculate the optimal choices of x and y and the lowest possible cost of producing Q=8. (o) Use your answers to parts (k) and (n) to plot two points on the firm's average cost curve. Do these points indicate that the firm has economies of scale or diseconomies of scale? For the last two parts, assume that the firm is committed to using equal quantities of X and Y (i.e., x=y), regardless of whether this is optimal. (p) Suppose that the firm produced the quantity of output that you found in part (j), using the x=y rule. How would this affect the firm's average cost per unit, compared to what you calculated in part (k)? How would this affect the firm's profit, compared to what you calculated in part (j)? (q) Solve the firm's optimization problem, assuming that the firm follows the x=y rule. How do the profit-maximizing price and quantity compare to the optimal point that you found in part (j)? How do its maximum attainable profits compare to the answer that you found in part (j)?

ECON 310: Problem Set #3 Please submit through Canvas Due Date: October 23, 2020 For all of the questions in this problem set, amume there is no tax at all. Stocks Consider stock A with a dividend yield equal to 2.5% (based on its dividend payments over the past year). The dividends are expected to grow at 8% per year. Stock A is currently traded at $52 per share. 1. According to Gordon's model, what would be the expected return on the stock? Answer: The Gordon's model states that 1+9 P = DI TE - 9 Rearrange the terms we get Pi(1+g) +9 = 2.5% . (1 +8%) + 8% = 10.7%% 2. Suppose the total dividends paid over the next year is $1.4 per share, leading to a downward revision of the expected dividend growth rate to 7.5%%, Assume the expected rate of return remains the same for this stock, what would be the actual rate of return from holding this stock over the next year? Answer: The price of stock A a year from now, according to Gordon's model, is 1+4 -14- 1+7.5% 10.7% -7:5%% =$47.03/share The rate of return is Rut - De + An -A 14+ 47.03-52 52 =-6.87% 3. Consider stock B which just paid $6 in dividends over the past year. The expected return on the stock is 12.5% and the stock is currently traded at $120 per share. At what rate are the dividends expected to grow for this stock according to Gordon's model? Answer: Again, starting with the Gordon's model 1+9 PEDITE - 9 and rearrange the terms we have Pi(TE - 9) = Di(1+ 9)calculating her debt payments-to-income ratio with and without the college loan. (Remember the 20 percent rule.) (LO5.3) 6. Joshua borrowed $500 for one year and paid $50 in interest. The bank charged him a $5 service charge. What is the finance charge on this loan? (LOS.4) 7. In problem 5, Joshua borrowed $500 on January 1, 2017, and paid it all back at once on December 31, 2017. What was the APR? (LO5.4) 8. If Joshua paid the $500 in 12 equal monthly payments in problem 5. what is the APR? (LO5.4) 9. Sidney took a $200 cash advance by using checks linked to her credit card account. The bank charges a 2 percent cash advance fee on the amount borrowed and offers no grace period on cash advances. Sidney paid the balance in full when the bill arrived. What was the cash advance fee? What was the interest for one month at an 18 percent APR? What was the total amount she paid? What if she had made the purchase with her credit card and paid off her bill in full promptly? (L05.4) 10. Brooke lacks cash to pay for a $600 washing machine. She could buy it from the store on credit by making 12 monthly payments of $52.74 each. The total cost would then be $632.88. Instead, Brooke decides to deposit $50 a month in the bank until she has saved enough money to pay cash for the washing machine. One year later, she has saved $642-$600 in deposits plus interest. When she goes back to the store, she finds that the washing machine now costs $660. Its price has gone up 10 percent-the current rate of inflation. Was postponing her purchase a good trade-off for Brooke? (L05.4) 11. What are the interest cost and the total amount due on a six-month loan of $1,500 at 13.2 percent simple annual interest? (L05.4) 12. After visiting several automobile dealerships, Richard selects the car he wants. He likes its $10,000 price, but financing through the dealer is no bargain. He has $2,000 cash for a down payment, so he needs an $8,ooo loan. In shopping at several banks for an installment loan, he learns that interest on most automobile loans is quoted at add-on rates. That is, during the life of the loan, interest is paid on the full amount borrowed even though a portion of the principal has been paid back. Richard borrows $8,ooo for a period of four years at an add-on interest rate of 11 percent. (LOS.4) a. What is the total interest on Richard's loan? b. What is the total cost of the car? TE E Focus + 100% Book Pro DN DD