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Suppose the representative household has the following utility function: U (C; l) = ln C +...

Suppose the representative household has the following utility function: U (C; l) = ln C + 0:5 ln l where C is consumption and l is leisure. The householdís time constraint is l+N=1 where Ns is the representative householdís labour supply. Further assume that the production function is Cobb-Douglas zK0:5 (N)0:5 where z = 1 and K = 1: 2.1 Assuming that the government spending is G = 0; use the Social Plannerís problem to solve for Pareto optimal numerical values C;l;N;Y (8 points). 2.2 Find the numerical values of the real wage rate w and of the representa- tive Örmís proÖt in a competitive equilibrium implementing the Social Plannerís (Pareto) optimal solution (4 points). 2.3 Draw a carefully labeled chart showing the impact of an increase in G on the Pareto Optimal allocation. Your chart does not have to be drawn exactly to scale. (7 points). 2.4 How would the optimal values C;l;Ns;Y;w; change (in what di- rection) in case if government spending increases (6 points)?

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Th Sociau plannexs Problem * to 0 5 C-N -N 0 S c·下出 ク W e 2 weTotal hour , max uswue( Budget constraint BL 3. BL of bna?e- PPF rae PPF Increase gover מ ment spending +na eeomom waoe rate

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