Arizona ECN 313 – Equilibrium with lump-sum taxation
Intermediate Macroeconomic TheoryHomework 4DUE 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 atthe hourly wage w and owns all the shares of the representative firm, as such it receives allfirm’s profits ?. The representative firm has a decreasing returns to scale (DRS) productionfunction, that is, Y = zH ? , with 0 < ? < 1. The government sector runs a balanced budgetsuch that G = T , where G is government purchases and T are lump-sum taxes paid by therepresentative 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 atthe hourly wage w and owns all the shares of the representative firm, as such it receives allfirm’s profits ?. The representative firm has a decreasing returns to scale (DRS) production1 function, that is, Y = zH ? , with 0 < ? < 1. The government sector runs a balanced budgetsuch that G = T , where G is government purchases and T = ?W wH are taxes paid by therepresentative 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 ?W increases? 2
