Suppose that one factory inputs its goods from two different plants, A and B, with different costs, 4 and 6 each respective. And suppose the price function in the market is decided as p(x,y)= 100−x−y where x and y are the demand functions and 0≤x,y0. Then as

x=

y=

the factory can attains the maximum profit,

Suppose you are reviewing a sheet for a bond portfolio and see the following information. These bonds have a par value of 100 and make semiannual coupon payments.

What is the yield to maturity of the bond portfolio based on the IRR calculation?

Suppose we are given the following information of a stock: S = 100, r = 5%, σ = 30%, and the stock doesn’t pay any dividend. Calculate the delta of a credit spread using two put options (strike price = $90 and $80) that matures in 0.5 year, based on BSM model.

A. 0.135

B. -0.135

C. 0.337

D. -0.337

You are the manager of a monopolistically competitive firm. the present demand curve you face is p=100-4Q. your cost function is cQ=50+8.5Q^2

a. What level of output should you choose to maximize profits?

b. What price should you charge?

c. What will happen in you market in the long run? explain

Mr. James has two coupon bonds with different maturities. Bond A has 10 years of maturity, while bond B has 30 years of maturity. Both the bonds have 10% coupon rates paid annually and a par value of $100. If the yield to maturity changes from 5% to 6%, what is the percentage change in the price of each bond?

a) Consider a one period binomial model with S(0) = 100, u = 1.2, d = 0.9, R = 0, pu = 0.6 and pd = 0.4. Determine the price at t = 0 of a European call option X = max{S(1) − 104, 0}.

b) If R > 0, motivate why the inequality (1 + R) > u would lead to arbitrage.

Can you solve it with hand solving, not the program solving?

Let us now assume that we have continuous time instead of discrete time, that S(0) = 100, r = 0.03, σ = 0.4 and T = 1. Calculate the price at t = 0 of the same European call option as above, i.e. X = max{S(1) − 104, 0}.

1. Mr. James has two coupon bonds with different maturities. Bond A has 10 years of maturity, while bond B has 30 years of maturity. Both the bonds have 10% coupon rates paid annually and a par value of $100. If the yield to maturity changes from 5% to 6%, what is the percentage change in the price of each bond?

Suppose we are given the following information of a stock: S = 100, r = 5%, σ = 30%, and the stock doesn’t pay any dividend. Calculate the delta of a credit spread using two put options (strike price = $90 and $80) that matures in 0.5 year, based on BSM model.

A. 0.135

B. -0.135

C. 0.337

D. -0.337

Peter buys a bond with a face value of $100, a time to maturity of four years, a coupon of 4% pa with semi-annual payments and a yield of 3% pa. Fifteen months later, the Reserve Bank of Australia unexpectedly increases the cash rate. The yield on Peter's bond increases to 3.5% pa. Peter sells the bond. Calculate the buying and selling price of the bond.