Consider the one-period model we learned in class. Suppose the representative consumer has prefer- ence over consumption (c) and leisure (l). Her indifference curves are represented by the following utility function: u(c;l) = 2ln(c) 2ln(l). Her time endowment is h = 1. The production function of the representative firm is given by Y = z(K)0.4(Nd)0.6 where the total factor productivity and capital are given by z = 1 and K = 1. Government collects tax of 1 in terms of consumption goods and has a balanced budget.

(1) What is the Pareto Optimum allocation of consumption, leisure, and aggregate output in this economy?

(2) What is the wage for the Pareto Optimal allocation to be supported as competitive equilibrium?

M_PS2_updated.pdf 1 Q Q 1 2 . ' @ Ed Q Suchen Seite 2 von 2 CULISUILICI S ULILILY ICVCI! M_PS2_update... 3. Consider the one-period model we learned in class. Suppose the representative consumer has prefer- ence over consumption (c) and leisure (1). Her indifference curves are represented by the following utility function: u(c;1) = 2In(c) + 2In(1). 2 Problem Set 2 Macroeconomics Her time endowment is h = 1. The production function of the representative firm is given by Y = z(K)0.4(Nd ) 0.6 I where the total factor productivity and capital are given by z = 1 and K = 1. Government collects tax of 1 in terms of consumption goods and has a balanced budget. (1) What is the Pareto Optimum allocation of consumption, leisure, and aggregate output in this economy? (2) What is the wage for the Pareto Optimal allocation to be supported as competitive equilibrium? OKT 14 4