Consumers must decide how much they wish to consume today (c.) versus in the future (c.)....

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Consumers must decide how much they wish to consume today (c.) versus in the future (c.). In making their decisions, they are constrained by the amount of their present income (v.) and future income (y.). Future income is related to present income in the following way: y = (1+g)y,, where g = the growth rate of income (1) The real interest rate in this economy is r 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(c.c,)=a In(c,)+(1-a)ln(c,) (2) The coefficients a and 1-a represent 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 d In(x) = dx/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, e,/y,. c) In Canada, the average propensity has been around 0.96 since 2000. Over that same period, real personal disposable income has grown by 24%, while real interest rates have averaged 24% (actually they quite a bit lower right now). Use your equation for APC to find the value of a for the Canadian economy. Based on that value, do Canadian consumers put more or less weight on present versus future consumption? Consumers must decide how much they wish to consume today (c.) versus in the future (c.). In making their decisions, they are constrained by the amount of their present income (v.) and future income (y.). Future income is related to present income in the following way: y = (1+g)y,, where g = the growth rate of income (1) The real interest rate in this economy is r 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(c.c,)=a In(c,)+(1-a)ln(c,) (2) The coefficients a and 1-a represent 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 d In(x) = dx/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, e,/y,. c) In Canada, the average propensity has been around 0.96 since 2000. Over that same period, real personal disposable income has grown by 24%, while real interest rates have averaged 24% (actually they quite a bit lower right now). Use your equation for APC to find the value of a for the Canadian economy. Based on that value, do Canadian consumers put more or less weight on present versus future consumption?