Question

QUESTION ONE a) A retired person's income comes from earnings on her savings of £200,000. The table below shows how she values different levels of income. Total Utility 12 22 Income 5,000 10,000 15,000 20,000 25,000 30,000 30 36 40 42 (ii) (i) Describe, using first and second derivatives, her attitude toward risk? Briefly explain. (10 marks) She is currently earning 10% on her £200,000 in a risk free investment. She has the choice of investing in a project that has a 40% probability of yielding a return of £30,000 return on her investment and a 60% probability of yielding $10,000 return on her investment. Will she be better off if she moved her £200,000 to the risky project? Explain. (10 marks) b) Consider an investment with three possible cash flow outcomes: £100 will be received with probability 0.1. £50 will be received with probability 0.2. £10 will be received with probability 0.7.

1. Describe, using first and second derivatives, her attitude toward risk? Briefly explain.

2. She is currently earning 10% on her £200,000 in a risk free investment. She has the choice of investing in a project that has a 40% probability of yielding a return of £30,000 return on her investment and a 60% probability of yielding $10,000 return on her investment. Will she be better off if she moved her £200,000 to the risky project? Explain.

Answer 1

a.i) As her income from savings doubles, the utility she derives less than doubles. She has diminishing marginal utility from the earnings.

first derivative= change in utility/ change in income= 22-10/10000-5000=0.002

and 30-22/15000-1000=0.0016

second derivative= (0.002-0.0016)/5000= 0.00000008

she is risk averse

a. ii) she is currently earning 10% of 200000= 20,000

investing in another project gives her expected payment of= 0.4*30,000+0.6*10000= 12000+6000=18000

since 20,000>18,000 she is better off without undertaking the new project.