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The economy lives for one period and has 1000 workers and a representative firm. The workers choose how much to consume and how much to work by maximizing the following utility function: ( , ) 8 l u c l c , where c is consumption and l is hours of leisure. The real wage rate is w units of output per hour, and workers have 168 hours available to them to allocate in a week. They work n hours, and do not have any other sources of income, so their budget constraint is c wn w(168 l) . The economy also has an aggregate production function represented as: Y F(K,N) 15K0.5N0.5 . The capital stock of the economy, K=7680 is owned by a single capitalist, who receives the entire accounting profit of the representative firm. a) (4 points) Prove that the labor supply of an individual worker can be written as nS 16w What is the aggregate supply of labor NS as a function of the real wage rate? b) (3 points) Prove that the aggregate demand for labor is 2 ND 432,000 w c) (3 points) If there are no imperfections inhibiting the functioning of the labor markets what is the equilibrium real wage and the equilibrium amount of employment (aggregate hours)? d) (2 points) How much does each worker work and how much do they consume? e) (5 points) Now assume that there is a minimum wage law that requires employers to pay at least 5 units of output per hour worked. Calculate aggregate labor demand and aggregate labor supply at this real wage. Illustrate the state of the labor market in a graph. (carefully label everything) ECO 320L Fall 2011, Professor Beatrix Paal due: Monday 10/10, in class Extra Credit Problem 1 2/2 f) (3 points) Assume that when there is an excess supply of labor, available hours are allocated between workers in the following way. Each worker is either employed or unemployed. When a worker is employed, the number of hours they work is equal to the number of hours they desire to work at the going real wage. When a worker is unemployed, they cannot work at all. With this assumption, calculate the hours worked by each employed worker, the number of employed (E) and the number of unemployed at the real wage w=5. g) (3 points) Calculate consumption of employed and unemployed workers when w=5. Calculate the unemployment rate. h) (3 points) Evaluate the welfare implications of this minimum wage policy from the perspective of both employed and unemployed workers. (Hint: compare numerically the utility of employed and unemployed workers under the minimum wage law to the utility of workers under free markets.) i) (4 points) If a worker does not know in advance whether they will or will not be employed when a minimum wage is introduced, will they be in favor or against this policy? (Hint: calculate expected utility assuming that the unemployment rate is the probability for any worker to be unemployed)