Intermediate Macroeconomic Theory Homework 4 DUE NOVEMBER 24 AT THE BEGINNING OF THE CLASS 1 Equilibrium with lump-sum taxation (50 points) A representative household has utility function U(C) = ln C; it supplies labor services at the hourly wage w and owns all the shares of the representative firm, as such it receives all firm’s profits π.

Intermediate Macroeconomic Theory Homework 4 DUE NOVEMBER 24 AT THE BEGINNING OF THE CLASS 1 Equilibrium with lump-sum taxation (50 points) A representative household has utility function U(C) = ln C; it supplies labor services at the hourly wage w and owns all the shares of the representative firm, as such it receives all firm’s profits π. The representative firm has a decreasing returns to scale (DRS) production function, that is, Y = zHα , with 0 < α < 1. The government sector runs a balanced budget such that G = T, where G is government purchases and T are lump-sum taxes paid by the representative household. The labor market is competitive. (A) Calculate equilibrium wage, w ∗ , labor, H∗ , consumption, C ∗ , and output Y ∗ ; (B) Show that the aggregate resource constraint C + G = Y holds; (C) How does C ∗ change if G increases? 2 Equilibrium with labor income tax (50 points) A representative household has utility function U(C) = ln C; it supplies labor services at the hourly wage w and owns all the shares of the representative firm, as such it receives all firm’s profits π. The representative firm has a decreasing returns to scale (DRS) production 1 function, that is, Y = zHα , with 0 < α < 1. The government sector runs a balanced budget such that G = T, where G is government purchases and T = τW wH are taxes paid by the representative household. The labor market is competitive. (A) Calculate equilibrium wage, w ∗ , labor, H∗ , consumption, C ∗ , and output Y ∗ ; (B) Show that the aggregate resource constraint C + G = Y holds; (C) How does H∗ change if τW increases? 2

Looking for a Similar Assignment? Order now and Get 10% Discount! Use Coupon Code "Newclient"