Please Explain

2. Suppose Households' receive a wage We for every hour they work and can invest in a bond, b with interest rate i. Suppose further that utility over work and consumption during the two periods is given by: log(e) - Lit 1 + 8 ( log(ca) - " IF 7 The household's lifetime budget constraint is: Pici(1 + i) + Pace = Will (1+0) + Walz (a) Set up the household's Lagrangian and find their inter-temporal (Euler) equations and their intra-temporal (labor supply) conditions. (b) There are no net-exports (the economy is closed), no government spending, and no capital. Therefore what is Y's equal to? Use this and the fact that 1 = F(L.) = Le to solve for wages as a function of output, It. (c) Use (b) to solve for Six and give intuition for your expression. (d) As y gets very close to zero, do wages become more responsive or less responsive to output? HINT: Plug y =0 into the expression from (c). (e) Recall that the Phillips Curve is given by: * = A (Y - P)+ A( E) + e Suppose y was very close to zero. Would we expect S, to be large or small? Explain intuitively