Question 3 a. A university student recieved $1,000 upon graduation at age 20 years. This person was hired by one of the largest global petrochemical companies soon after graduation with an expected annual income of $250. Assume that the retirement age is 65 years and life expectancy is 85 years in the country in which the student resides. Given that this country has zero real interest rate and consumption smoothing is optimal for all Individuals: 1. Derive an expression for the person's lifetime resources clearly describing each term. [2 marks) ii Calculate the value of the person's lifetime resources. [1 mark] Derive an expression for the person's consumption function clearly describing any new terms included, 14 marks) iv. Derive an expression for the person's average propensity to consume. [2 marks) State the theory on which you based the calculations in parts i., li. and ill. above. [1 mark] vi. State in one sentence how the consumption puzzle is addressed in the theory stated in part v. above. [2 marks] v. b. For another individual, current annual income is $150 of which 30% is earned through lottery winnings. If this person tends to spend 80% of his annual salary, Calculate the value of this person's estimated annual salary. [2 marks] li Derive an expression for this person's consumption function clearly describing each term [2 marks] Derive and expression for this person's average propensity to consume clearly describing any new terms included. [1 mark] iv. State the theory on which you based your answers for parts i, and ill. above. [1 mark] State in one sentence how the consumption puzzle is addressed in the theory stated in partiv, above, [2 marks] O BE