1. Suppose a public referendum is being held on whether or not to levy a tax on cigarettes. Currently, the supply of cigarettes is given by Qs = -100 + 6P. You estimate the demand for cigarettes to be Qd = 200 - 2P.

You are asked to evaluate the likely effects of a tax on cigarettes equal to $10 per pack of cigarettes. Specifically, you are to file a report which predicts by how much this will reduce the amount of cigarettes sold. You are also asked to estimate the proportion of the tax that will be paid by the cigarette companies (sellers), and the proportion of the tax that will be paid by the smokers (consumers) of cigarettes.

To do this, you will first need to calculate the current price and quantity of cigarettes sold.

a) (6 points) What is the equilibrium price and quantity of cigarettes?

Next you know from your economics class that you will need to know the price elasticity of demand and the price elasticity of supply of cigarettes. (Note: for parts b-e, please leave your answers in the form of a fraction.)

b) (6 points) What is the price elasticity of demand for cigarettes at the equilibrium price?

c) (6 points) What is the price elasticity of supply of cigarettes at the equilibrium price?

Using your answers to b) and c), you are now able to determine what proportion of the tax will be paid by buyers, and what proportion of the tax will be paid by sellers.

d) (6 points) What proportion of the tax will be paid by sellers?

e) (6 points) What price will buyers pay after the tax is imposed?

f) (6 points) What quantity of cigarettes will be sold after the tax?

Finally, a new proposal suggests that the tax should be levied on the cigarette companies instead of the smokers.

g) (6 points) From what you have learned in this class, how should you respond to this proposal?

Suppose a public referendum is being held on whether or not to levy a tax on cigarettes. Currently, the supply of cigarettes is given by Qs = -100 + 20P. You estimate the demand for cigarettes to be Qd = 200 - 5P.You are asked to evaluate the likely effects of a tax on cigarettes equal to $1 per pack of cigarettes. Specifically, you are to file a report which predicts by how much this will reduce the amount of cigarettes sold. You are also asked to estimate the proportion of the tax that will be paid by the cigarette companies (sellers), and the proportion of the tax that will be paid by the smokers (consumers) of cigarettes.To do this, you will first need to calculate the current price and quantity of cigarettes sold.a) (6 points) What is the equilibrium price and quantity of cigarettes? Next you know from your economics class that you will need to know the price elasticity of demand and the price elasticity of supply of cigarettes. (Note: for parts b-e, please leave your answers in the form of a fraction.)b) (6 points) What is the price elasticity of demand for cigarettes at the equilibrium price?c) (6 points) What is the price elasticity of supply of cigarettes at the equilibrium price?Using your answers to b) and c), you are now able to determine what proportion of the tax will be paid by buyers, and what proportion of the tax will be paid by sellers.d) (6 points) What proportion of the tax will be paid by sellers?e) (6 points) What price will buyers pay after the tax is imposed?f) (6 points) What quantity of cigarettes will be sold after the tax??Finally, a new proposal suggests that the tax should be levied on the cigarette companies instead of the smokers.g) (6 points) From what you have learned in this class, how should you respond to this proposal?

The spot price of an investment asset is $30 and the risk-free rate for all maturities is 10% with continuous compounding. The asset provides an income of $2 at the end of the first year and at the end of the second year. What is the three-year forward price? (Hint: First find the PV of $2 income at year 1 and year 2 using 10% rate and subtract it from spot price.)

The spot price of an investment asset is $30 and the risk-free rate for all maturities is 10% with continuous compounding. The asset provides a dividend income of $2 at the end of the first year and at the end of the second year. What is the three-year futures price? (Hint: you would first need to find the PV of year 1 and year 2 incomes and then subtract it from  the spot price.)

A) You try to price the options on XYZ Corp. The current stock price of XYZ is $100/share. The risk-free rate is 5%. You project the stock price of XYZ will either be $90 or $120 in a year. Assume you can borrow or lend money at the risk-free rate. Use risk-neutral approach to price the 1-year call option on XYZ Corp with the strike price of $105. (Attention: using a wrong approach will cost you all the credits)

B) You try to price the options on XYZ Corp. The current stock price of XYZ is $100/share. The risk-free rate is 5%. You project the stock price of XYZ will either be $90 or $120 in a year. Assume you can borrow or lend money at the risk-free rate. Use risk-free portfolio approach to price the 1-year put option on XYZ Corp with the strike price of $105. (Attention: using a wrong approach will cost you all the credits)

C) Use put-call parity to verify the call and put option prices you just calculated in A and B

The current price of a stock is $40. The price of a one-year European put option on the stock with a strike price of $30 is quoted at $2 and the price of a one-year European call option on the stock with a strike price of $50 is quoted at $3.

1. (2 points) Investor D wants to own the shares but wants to reduce his initial investment cost. So he buys the stock and shorts the call option on 100 shares.
   1. Draw a diagram illustrating how the investor’s profit varies with stock price. What are his max profit and max loss per share?
   2. Compute his dollar profit and return if the share price is $25, $42, or $56 in one year.
2. (2 points) Investor E wants to bet on the possible share price fluctuations in the coming year. He buys the put option and the call option on 100 shares.
   1. Draw a diagram illustrating how the investor’s profit varies with stock price. What are his max profit and max loss per share?
   2. Compute his dollar profit and return if the share price is $25, $42, or $56 in one year.

Sam buys 100 shares of Acme stock at $100 per share on January 1, Year 1. At the end of the first year (December 31, Year 1), she buys 100 more shares at $120 per share. At the end of the second year (December 31, Year 2), she buys another 100 shares for $135 per share. The stock pays a dividend of $2.00 per share on December 29th of each year. Acme is trading at $169.80 as of December 31, Year 3. What is the time weighted return for Acme since January 1, Year 1 to today?

5. There are 100 patients who could benefit from a new drug, Tipilor, manufactured by Zifer. Patient i has willingness to pay i, i=1,…,100. Ignore fixed costs and assume marginal cost, c, is constant.

a) What is the profit maximising price and resulting profit?

b) Now assume all patients have insurance which means they only pay 10% of the price as a co-payment. What is the profit maximising price and resulting profit?

c) Zifer sets up a charity to cover the co-payment for poor people. Patients 1, 2, …, 50 are considered poor. What is the profit maximising price and resulting profit?

d) For c = 10, calculate optimal profit in a), b) and c) and conclude whether setting up the charity is profitable.

There are 100 patients who could benefit from a new drug, Tipilor, manufactured by Zifer. Patient i has willingness to pay i, i=1,…,100. Ignore fixed costs and assume marginal cost, c, is constant.

a) What is the profit maximising price and resulting profit?

b) Now assume all patients have insurance which means they only pay 10% of the price as a co-payment. What is the profit maximising price and resulting profit?

c) Zifer sets up a charity to cover the co-payment for poor people. Patients 1, 2, …, 50 are considered poor. What is the profit maximising price and resulting profit?

d) For c = 10, calculate optimal profit in a), b) and c) and conclude whether setting up the charity is profitable.

5. There are 100 patients who could benefit from a new drug, Tipilor, manufactured by Zifer. Patient i has willingness to pay i, i=1,…,100. Ignore fixed costs and assume marginal cost, c, is constant.

a) What is the profit maximising price and resulting profit?

b) Now assume all patients have insurance which means they only pay 10% of the price as a co-payment. What is the profit maximising price and resulting profit?

c) Zifer sets up a charity to cover the co-payment for poor people. Patients 1, 2, …, 50 are considered poor. What is the profit maximising price and resulting profit?

d) For c = 10, calculate optimal profit in a), b) and c) and conclude whether setting up the charity is profitable.

[25 marks]