Please refer to the attachments below to answer the questions below appropriately.

2. Consider the following lifetime optimal consumption-saving problem IM - B' In a (11) subject to Oil - R(-4).1=0...T (12) 40 = 4 (0). ar+1 20. (13) where 8 is the consumer's rate of time preference (B $ 1) and R = 1 +r is the gross interest rate. (a) Use the flow budget constraints, (12), and the terminal condition to derive the intertemporal (lifetime) budget constraint.(b) Derive the consumption Euler equation that links consumption in two consecutive periods, { and { + 1; and then combine it with the intertemporal budget constraint to find optimal consumption (c) as a function of the given initial level of asset holdings (ag), model parameters (R, S, T), and time f.An equity pays half-yearly dividends. A dividend of d per share is due in exactly 3 months' time. Subsequent dividends are expected to grow at a compound rate of g per half year forever. (i) If i denotes the annual effective rate of return on the equity, show that P, the price per share, is given by: P=- d(1+1) [3] (1+1)" - (1+g) The current price of a share is $3.60, dividend growth is expected to be 2% per half year and the next dividend payment in 3 months is expected to be 12p. Calculate the expected annual effective rate of return for an investor who purchases the share. [3] [Total 6]