2. Why do Europeans work less than Americans? Consider an economy populated by a representative consumer, a representative firm, and a government. Suppose that consumers preferences are defined over consumption and labor as U = ln C (Ns)2 2 where > 0 is a preference parameter related to the disutility of work. The consumer supplies labor at the real wage w and earns dividends . In addition, she pays labor income taxes at the tax rate 0 < < 1, and lump-sum taxes (T > 0). Her budget constraint is C = (1 )wNs + T The firm chooses work time to maximize profits, = Y wNd, and uses a technology given by Y = zF(K,Nd) = z Nd to produce the consumption good, where 0 < < 1 is an exogenous technological parameter. Note that the capital stock is K = 1, for simplicity. The government uses all the taxes to finance government expenditure G. Thus, its budget constraint is G = wN + T . In this model, the exogenous variables are K, z, , , G, and . The rest of variables are endogenous. (a) Formulate the consumers maximization problem, the corresponding Lagrangean function, and derive the first-order conditions (FOCs) with respect to C and Ns. Derive the labor supply. (b) Formulate the firms maximization problem and derive the first-order condition. Derive the labor demand. (c) Find the solution for N and w. Draw a supply-demand diagram for the labor market of this model. Label the equilibrium values of w and N. (d) Consider two economies: A and E. The only difference is that individuals in A pay a lower labor income tax rate than do individuals in E: A < E. Other things equal, can this difference in taxes explain why individuals in A work more than individuals in E? Justify mathematically or graphically. (e) Assume now that we have two economies: A and E. The only difference is that individuals in A have a lower disutility of work than do individuals in E: A < E. Other things equal, can this difference in preferences explain why individuals in A work more than individuals in E? Justify mathematically or graphically.