what are the identified issues?

Consider the TwoPeriod Endowment Model of household behaviour studied in class. The household derives utility from oonsumption today c and consumption tomorrow 5'. Suppose that preferences are represented by the utility function Life a\") = {at + ts\")? where d E [(1.1). The household receives exogenous inoome y today and y\" tomorrow. For simplicity. assume that there are no lumpsum taxes {i.e. t = t' = I]. using the notation in class]. The real interest rate is given by r. (1} [7 marks] Write down the problem of the household. (2} [7 marks] Show that the optimal level of consumption in the first period is given by: we =1+x3?[1+r}' where we a y + iiir denotes lifetime wealth. Ci (3} [7 marks] Suppose that the parameters of the model take the following values: p = soc, y\" = 105. , = [1.95. r = . Based on these values. is the household a lender or a borrower? Justify your answer. (4} [7 marks] Suppose that now the interest rate r' increases to {1.10 {while the values of all other parameters are unchanged). How would this change optimal consumption in the first period of? What does your finding imply about the relative magnitudes of income and substitution effects? Explain. (5} [7 marks] Using a diagram on the {c.c'} plane. illustrate the effect of an increase in r on the optimal consumption bundle of the household. and identify income and substitution effects. Would the consumer be betteroff or worseoff after the increase in the interest rate? Note: To answer Part {5]. you don \"t need to do any algebra or calculations