BXP is currently trading at $91/share. You bought 6 CALL-option contracts on BXP with a strike price of $90 for $4.0 each and sold 6 CALL-option contracts on BXP with a strike price of $100 for $2.0 each.

a. What will be your total $ and % gain/loss if BXP price is $102 at the expiration date?

b. What will be your total $ and % gain/loss if BXP price is $85 at the expiration date?

c. What will be your total $ and % gain/loss if BXP price is $94 at the expiration date?

Assume that the price S of a risky asset follows a binomial model with S(0) =
$100, u = 10% and d = -10%. The underlying asset pays a dividend of $5 on the odd times, i.e., 1; 3; 5...,
and only if the price is strictly higher than $95. In this market, the risk-free rate is 0% (zero).

You are called to price a European call with strike price K = 87 and expiry date N = 3 with the additional
restriction that during the life of the call the stock price has not exceeded the value of $110.

1. The representative consumer (the consumer that his basket of goods is the same as the "average" basket consumed by city dwellers) consumes two goods: Apple and oranges. The price of oranges is 1 dollar per unit and the price of apples is 2 dollars per unit. In year 1 the representative consumer consumed 10 units of oranges and 10 units of apples. The basket in year 1 is used to compute the CPI.

(a) In year 2 the price of oranges went up to 1.1 dollars per unit and the price of apples went up to 2.2 dollars per unit. What is the percentage change in the consumer price index (CPI)?

(b) Assume that income went up in year 2 and the income of the representative consumer is equal to the price of the basket that the consumer bought in year 1. What is the basket that is chosen by the representative consumer in year 2?

(c) Compare the welfare of the consumer in year 2 to his welfare in year 1.

2. Answer question 1 under the assumption that in year 2 the price of oranges went up to 1.2 dollars per unit but the price of apples did not change.

(a) What is the percentage change in the consumer price index (CPI)?

(b) Assume that the income of the representative consumer in year 2 is equal to the price of the basket that the consumer bought in year 1. Compare the basket chosen in year 2 to the basket chosen in year 1.

(c) Compare welfare in year 2 to welfare in year 1.

3. A consumer lives for two periods. His income in period 1 is !Y1 and his income in period 2 is Y . The consumer is free to lend and borrow at zero interest rate ( r =0

!

(a) What is the price of consumption in period 1 in terms of consumption in period 2? (How many units of period 2 consumption must the consumer give up to get an additional unit of consumption in period 1)?

(b) What is the maximum consumption that the consumer can have in the first period?

(c) Draw the budget constraint. In your graph have the endowment point, the slope and the intersections with the horizontal axis and with the vertical axis.

! 2 and!R=1+r=1).!Y1 =Y2 =10.

(d) The government introduces a tax of !T1 =5 in the first period. Use the graph in (c) to show the change in the budget line.

(e) How will the tax effect the consumer's consumption in the first period? How will it effect the consumer's consumption in the second period? (Assume that both goods are normal).

(f) Will the consumption in the first period change by more than 5 units? Why?

(g) Assume now that the government decides to impose the tax in the second period rather than the first. Will this change the budget line? Will this change the choice of consumption?

(h) Assume that initially government spending was zero in both periods. Then the government increased its spending in the first period to G =5 and financed it by

!
taxes of 5 units in the first period. What will happen to national savings? Explain.

4. Answer question 3 under the assumption that !r =0.1 (and !R =1.1 ). To simplify the calculations assume: Y =Y =11 . The questions are repeated here with slight

changes.

!1 2

(a) What is the price of consumption in period 1 in terms of consumption in period 2? (How many units of period 2 consumption must the consumer give up to get an additional unit of consumption in period 1)?

(b) What is the maximum consumption that the consumer can have in the first period?

(c) Draw the budget constraint. In your graph have the endowment point, the slope and the intersections with the horizontal axis and with the vertical axis.

(d) The government introduces a tax of !T1 =5 in the first period. Use the graph in (c) to show the change in the budget line.

(e) How will the tax effect the consumer's consumption in the first period? How will it effect the consumer's consumption in the second period? (Assume that both goods are normal).

(f) Will the consumption in the first period change by more than 5 units? Why?

(g) Assume now that the government decides to impose the tax in the second period rather than the first. Will this change the budget line? Will this change the choice of consumption? (Hint: the tax remains 5 units and not 5.5)

(h) Assume that initially government spending was zero in both periods. Then the government increased its spending in the first period to G =5 and financed it by

!
taxes of 5 units in the first period. What will happen to national savings? Explain.

According to a recent survey, a random sample of 100 homes sold in the Baton Rouge metro area had an average sale price of $263,000. If the population standard deviation of home prices is $20,000, what is the 99% confidence interval of the true population average sales price for homes sold in Baton Rouge?

Suppose you invest in 100 shares of Harley-Davidson (HOG) at $40 per share and 200 shares of Yahoo (YHOO) at $25 per share. If the price of HOG increases to $50 and the price of YHOO decreases to $12 per share, what is the return on your portfolio? (Assume no dividends on either stock).

Suppose that the inverse demand function, marginal revenue, marginal cost and total cost for a gizmo product produced by a monopolist are as follows:

P = 100 - 2Q

MR = 100 - 4Q

MC = 2

TC = 10 + 2Q

a. Find the monopolist's profit-maximizing output and price.

b. calculate the monopolist's profit/losses, if any.

c. What is the Lerner Index for this industry.

suppose that the inverse demand function, marginal revenue, marginal cost and total cost for a gizmo product produced by a monopolist are as follows

p=100 -2Q

MR= 100-4Q

MC=2

TC=10+2Q

a. Find the monopolist's profit maximizing output and price.

b. Calculate the monopolist's profit/loss ,if any

c. What is the Lerner Index for this industry

Consider a 3-year maturity annual 9% coupon paying bond with a YTM of 12%.

a. What is the Duration of this bond?

b. What will be the predicted price of this bond if the market yield increases by 100 basis points. [Remember, 100 basis points = 1% point]? You must use the duration (calculated in the part above) to get full points for this question.

The following table shows the short-run cost data of a perfectly competitive firm. Assume that output can only be increased in batches of 100 units.

a. Explain how a firm chooses quantity to maximise profit in a competitive market.

b. What is the firm’s fixed cost? (1 mark)

c. Suppose that market price is $8. What is the profit maximising level of output

d. Suppose that market price is $8. What is the firm’s profit?

e. Suppose the fixed cost of production rises by $500 and the price per unit is still $8. What happens to the firm’s profit-maximising output level?

f. What is the price level below which the firm will not produce in the short run?

1. Consider two firms, Firm A and Firm B, who compete as duopolists. Each firm produces an identical product. The total inverse demand curve for the industry is P=250-QA+QB. Firm A has a total cost curve CAQA=100+QA2. Firm B has a total cost curve CBQB=100+2QB.
   1. Suppose for now, only Firm A exists (QB=0). What is the Monopoly equilibrium quantity and price? What is Firm A’s profit?
   2. Find the Nash Cournot equilibrium price and output level. What are the firms’ profits?
   3. Find the equilibrium price and output level in the market if firm A acts as a Stackelberg leader. What are the firms’ profits?
   4. Suppose that the two firms are able to form a cartel. Derive the output each firm will produce, the market price, and the total profit under the cartel solution.
   5. Compare the Cournot, Stackelberg, and Cartel outcomes to the monopoly outcome you calculated in part a.