4. money in a doo to put aside for a year. She can put the money in a bank is f

Question

4. money in a doo to put aside for a year. She can put the money in a bank is f interest. Alternatively she can take a risk company. Each share costs £4, and account which is perfectly safe but which as a zero rate o by buying shares in a Jane thinks that with probability after of 0.5 that the price will fall to £2. (No dividends are to be paid.) 0.5 the price will rise to £10 a year. However, she also thinks there is a probability (a) and Define what is meant by state contingent wealth, write down the prospects Jane faces if she puts all her money in the bank or alternatively if she buys 100 shares (b) Suppose she buys x shares. Write down her wealth in the good state, Wg (when price goes up), and in the bad state Wb. Using this information derive the equation of her budget constraint over Wg and W (c) Define clearly and precisely what is meant by risk aversion. Jane is an expected utility maximiser, and is risk averse. Explain how you would verify that this s so. (d) Using a diagram, explain why the information given so far enables you to predict that Jane will take a gamble and purchase some shares. Why does she do this if she is risk averse?

Explanation / Answer

a)state contingent is a type of contract which is implemented only when a particular state of nature occurs. For example in the case of car accident, the insurer pays only if an accident occurs.Jane can put all her money in the bank in which case she wont earn any interest. The other possibilities are that she can put x % of her money in the bank and (1-x)% in the shares. The amount invested in the shares can cause her profit or loss where uncertainty is involved.

b) Given that Jane buys x shares. In the good state, her increased profit is x(10-4)=6x and the total wealth is 6x+4x=10x. In the bad state, her loss is x(4-2)=2x.Her total wealth in this situation is 4x-2x=2x.So Wg=10x and Wb=2x. So the budget constraint is (0.5 )10x+(0.5)2x

c)Risk aversion is the behaviour of the consumers and investors to reduce the uncertainty. In such cases they mostly prefer a predictable payoff with possibly lower expected payoff rather than unknown payoff with a more expected payoff.

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