Suppose there are two firms in an instant coffee market. Market demand curve is given by P = 100 – 2Q, and marginal cost of production for both firms are equal and constant at m=12.

a) Find the output that will maximize firm’s profit if the two firms choose price simultaneously. What is the price that the firm will charge and how much is the profit of each firm?

b) Find the output that will maximize firm’s profit if two firms choose quantity simultaneously. What is the price that they will charge and how much is the profit of each firm?

c) Suppose the quantity game as in (b) is played by the firm over and over again times. Compute the revenue matrix for these firms where two actions are possible taken by the firm is either cooperative or non-cooperative. Based on the resulting matrix, calculate the possible discount factor value the two firms continue to work together.

Suppose there are two firms in an instant coffee market. Market demand curve is given by P = 100 – 2Q, and marginal cost of production for both firms are equal and constant at m=12.

a) Find the output that will maximize firm’s profit if the two firms choose price simultaneously. What is the price that the firm will charge and how much is the profit of each firm? ( 10 marks)

b) Find the output that will maximize firm’s profit if two firms choose quantity simultaneously. What is the price that they will charge and how much is the profit of each firm? ( 15 marks)

c) Assume the quantity game as in (b) is played by the firm repeatedly. Formulate a revenue matrix for these firms where two actions a firm can take are either cooperative or non-cooperative. Based on the resulting matrix, calculate the value of the discount factor that allows the two firms to work together. ( 20 marks)

Suppose a competitive firm has a short-run cost function: C(q) = 100 + 10q − q^2 + q^3 , where q is the quantity of output.

1. Is this a short-run or a long-run cost function? Explain.

2. Find the firm’s marginal cost function: MC(q).

3. Find the firm’s average variable cost function: AVC(q).

4. Find the output quantity that the firm AVC at the minimum. Does the MC increasing or decreasing before the quantity. And does the MC increasing or decreasing after the quantity?

5. Suppose the firm maximizes profit, and the market price is $40. How much would the firm produces? How about if the market price is $20.

6. Plot MC, AVC, and the firm supply curve. Label firm’s profit, revenue and cost when the market price is at $40.

Use the information from the preceding table to fill in the following table.

From 2013 to 2014, nominal GDPdecreased   , and real GDPdecreased   .

The inflation rate in 2014 was _______ .

Why is real GDP a more accurate measure of an economy's production than nominal GDP?

Real GDP is not influenced by price changes, but nominal GDP is.

Real GDP does not include the value of intermediate goods and services, but nominal GDP does.

Real GDP includes the value of exports, but nominal GDP does not.

1. Prepare the journal entries that would be recorded using a periodic inventory system.

2. Prepare the journal entries that would be recorded using a perpetual inventory system, including any “book-to-physical” adjustment that might be needed.

Problem 1: Evaluation of a known integral using various quadratures: In this problem, we are going to compute the price of a European call option with 3 month expiry, strike 12, and implied vol 20, Assume the underlying is 10 now and the interest rate is 4%.

1. Use Black-Scholes formula to compute the price of the call analytically.

2. Calculate the price of the call numerically using the following 3 quadrature methods:

(a) Left Riemann rule

(b) Midpoint rule

(c) Gauss nodes of your choice (say explicitly why you made that choice) with the number of nodes N = 5, 10, 50, 100 and compute the calculation error as a function of N for each of the methods.

3. Estimate the experimental rate of convergence of each method and compare it with the known theoretical estimate.

4. Which method is your favorite and why

Your company currently sells its product with a 3% discount to customers who pay cash immediately. Otherwise the full price is due within 30 days. Half of your customers take advantage of the discount. You are considering dropping the discount so that your new terms would just be net 30. If you do that, you expect to lose some customers who were only willing to pay the discounted price, but the rest will simply switch to taking the full 30 days to pay . Altogether, you estimate that you will sell 40 fewer units per month (compared to 500 units currently). Your variable cost per unit is $60 and your price per unit is $100. If your required return is 1% per month, what is the change in value after you switch to the new credit policy

A newly issued bond has a maturity of 10 years and pays a 5.5% coupon rate (with coupon payments coming once annually). The bond sells at par value.

a. What are the convexity and the duration of the bond? Use the formula for convexity in footnote 7.
b. Find the actual price of the bond assuming that its yield to maturity immediately increases from 5.5% to 6.5% (with maturity still 10 years). Assume a par value of 100.
c. What price would be predicted by the modified duration rule ΔPP=−D*Δy?ΔPP=−D*Δy? What is the percentage error of that rule?
d. What price would be predicted by the modified duration-with-convexity rule ΔPP=−D*Δy+12×Convexity×(Δy)2?ΔPP=−D*Δy⁢+12×Convexity×(Δy)2? What is the percentage error of that rule?

1. You purchase an interest rate futures contract that has an initial margin requirement of 9% and a futures price of $130,538. The contract has a $100,000 underlying par value bond. If the futures price falls to $126,500, you will experience a ______ loss on your money invested.

Multiple Choice

A 24.00%

B 57.37%

C 45.37%

D 34.37%

2. Malmentier SA stock is currently priced at $120, and it does not pay dividends. The instantaneous risk-free rate of return is 7%. The instantaneous standard deviation of Malmentier SA stock is 40%. You want to purchase a put option on this stock with an exercise price of $125 and an expiration date 30 days from now. According to the Black-Scholes OPM, you should hold __________ shares of stock per 100 put options to hedge your risk.

A 21

B 25

C 60

D65

Use the following data for questions 8-10. Assume an initial margin requirement of 55% and maintenance margin of 40%. An investor has $5,500 in cash and wishes to purchase ABC stock. ABC is currently trading at $100 per share and your broker charges 7.5% interest on margin loans for the period.

8. What is the return on equity of the margin position after one year when price rises to $120? (a) 20.23% (b) 30.23% (c) 40.23% (d) None of the above

9. What is the return on equity of the margin position after one year when price falls to $80? (a) 20% (b) 42.5% (c) 80% (d) None of the above

10. At what price would you receive a margin call (ignore the interest on margin loan)? (a) $75 (b)$60 (c) $120 (d) None of the above

I need to show work.