where w, depicts the wealth of the household. (d) Why has this solution been refereed to as the "permanent income hypothesis"? (e) Use the consumption function to illustrate the effects on current consumption of a perma- nent increase in income. (f) Compare your answer in (e) to a temporary change in income expected to occur in period 1 + 2. (g) What policy implications might result as a consequence of those differences? Using the households' Euler equation, in class we showed that the growth rate of consumption on the optimal path is given by: r-0 (h) Determine how the growth rate of consumption depends on the relative size of r and e. (i) Determine the equilibrium solution and explain why any other solutions will not be sustainable in the long run. Question 4 A decentralized economy with labour leisure choice, a government, port- folio choice and labour\\ capital income taxation. An infinitely lived representative household enjoys consumption and leisure stream {, , ], which is evaluated by: V, = 28 /(c,, 1,)# c (0, 1) is the discount factor and U( , ) is increasing, strictly concave, and three times continuously differentiable in both arguments. The household is endowed with one unit of time that can be used for leisure , and labor n,: I, tn, =1 One unit of labor time earns the average wage rate w. The household can save in capital as sets k, which carn the interest rate r, and depreciate at rate / c (0, 1). Similarly, the household can also save in one-period bonds issued by the government. Let R, denote the gross rate of return on one-period bonds held between { and f + 1. In addition, the household pays taxes on both income from labor and income from capital assets