way : y = (1+ g)y where g = the growth rate of income (1) The real interest rate in this economy is / and individuals can lend and borrow at this rate. a) Use the above information to derive first the households' level of consumption in period 2 and then their inter-temporal budget constraint. b) Using logs, the inter-temporal utility function of the representative consumer is given by: In(q, c,) = aln(c)+ (1- @) In(c,) (2) The coefficients a and 1- arepresent the weights placed on present and future consumption. [Hint: In doing the question, remember for any variable x, that the derivative of the natural log is given by aln(x) = ddx/x.] 1) Starting with the inter-temporal utility function (equation (2)), find the algebraic relationship between present and future consumption that maximizes utility (In(c. c)). 2) Then, using that relationship, find an equation for present consumption as it relates to only present income, wealth and the real interest rate. 3) Next, find an expression for the average propensity to consume (APC], defined as current consumption divided by current income, s /y