eco204_HW_21 - University of Toronto, Department of...

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Unformatted text preview: University of Toronto, Department of Economics, ECO 204 2008‐2009 S. Ajaz Hussain ECO 204 2008‐2009 Ajaz Hussain HW 21 Question 1 (2007‐2008 Final Exam question) You’re a dealer for a brand of luxury cars “Lamb‐boo‐Genie” 1 Sales of Lamb‐boo‐Genie cars are pro‐cyclical: in a growing (G) economy sales increase and in a recessionary (R) economy sales decrease. You have to place an order tomorrow afternoon for either 50 or 100 cars. Your profits depend on the state of the economy: Lamb‐boo‐Genie Dealership Profits Growth (G) $225m $350m Order Size 50 Cars 100 Cars Recession (R) $100m ‐$150m (a) Suppose the probability of growth is P(G) = 0.6. How many cars should you order? Assume you’re a risk neutral decision maker. (b) To help decide how many cars to order, you pay money to acquire some information about the stock market which better informs you whether the economy will grow or contract. The following table gives the probability of stocks rising and falling and the economy growing and contracting: Table of Probabilities Growth (G) Recession (R) 0.4875 0 0.1125 0.4 0.6 0.4 Stock Market Stocks Rise (+) Stocks Fall (‐) Total 1 Total 0.4875 0.5125 1.000 No relation to Lamborghini. 1 University of Toronto, Department of Economics, ECO 204 2008‐2009 S. Ajaz Hussain What is the value of your decision if you use the stock market as a “test” for whether the economy will grow or go into a recession? How much is the stock market information above worth to you? Again, assume you are risk neutral. Show all calculations clearly. Question 2 In Lecture 23 we derived the actuarially fair price of insurance using the argument that if an insurance company is to ensure that it has sufficient funds on its books to cover payout then: Funds on books = Expected Payout → Insurance premium on books = Expected insurance claims → (Price per dollar of insurance)*(Insurance amount) = (Probability of loss)*(Insurance amount) → Price per dollar of insurance = Probability of loss In this question you will derive the same result through a different approach. Suppose all customers of an insurance company purchase an insurance policy worth $X. That is, if the “event” (such as an accident, fire or death) occurs, the insurance company will pay the customer $X. Let the probability of the event be p. Suppose the insurance policy premium costs $P (don’t confuse P and p!). That is, this is how much money a customer pays the insurance company to purchase the insurance policy $X. This implies that the price per dollar of insurance is $P = price per dollar of insurance * $X Denote the price per dollar of insurance as “price/$”. (a) What are the expected profits of the insurance company? (b) Suppose the insurance industry is perfectly competitive. What are the expected profits in the long run? Prove that the price per dollar of insurance is the probability of loss. Question 3 (2007‐2008 Test 2 question) Mr. S. Hussein, a distant relative of Saddam Hussein, owns a very expensive home worth $1.5m Saddam left Mr. S. Hussein a vast sum of money). Mr. A. Hussain, unrelated to Saddam Hussein, owns a cheap home (more like a hut actually) worth $10,000. A newspaper reporter creates a scandal by reporting that the price per dollar of insurance is the same for Mr. S. Hussein and Mr. A. Hussain. She argues that the insurance company is discriminating against Mr. A. Hussain. As the economist lawyer representing the insurance company, can you give a 2 University of Toronto, Department of Economics, ECO 204 2008‐2009 S. Ajaz Hussain simple explanation for why Hussein and Hussain may be paying the same price per dollar of insurance? A two sentence answer suffices. 3 ...
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