1 Consider two workers with identical preferences, Brian and lan. Both have the same life cycle wage path-in other words, they face the same wage at every age and they know what their future wages will be. Leisure and consumption are both normal goods a. On a graph. compare the life cycle path of hours of work for Brian and lan if Brian receives an unexpected inheritance at age 35. Give a brief intuitive explanation of the graph. b. On a graph. compare the life cycle path of hours of work for Brian and lan if instead Brian has always known that he will receive (and, in fact, does receive) a one-time inheritance at age 35. . Give a brief intuitive explanation of the graph. c. Next. compare the life-cycle path of hours of work for Brian and lan if instead Brian receives an unexpected wage increase at age 35. Give a brief intuitive explanation of the graph. 2. Suppose that The Acme Widget Co. uses capital (K) and labor (E) to produce widgets, and that the production function for widgets is given by Q= Q=K1/3E 1/2. Suppose that r=$1 and w=$4, where r is the price of capital and w is the wage rate. Finally, suppose also that the price of widgets, p. is $8. a. Derive the marginal product of labour (MPE ) and the marginal product of capital (MPK). Clearly show your work. b. Suppose K=8 in the short run, plot this firm's short-run labor demand curve. c. Given that w=4. how many workers should this firm hire in the short run? Clearly show your work. d. What are the firm's profits in the short run? Clearly show your work. 3. In January, General Motors laid off 2.000 workers. Suppose you are hired as a consultant to estimate the impact of these layoffs on the number of cars that GM will be able to produce this year. To do so, you need to estimate the marginal productivity of workers at GM. You go to the company's web page and learn that the company pays the average worker $140,000 per year and is able to sell the average car for $20,000. If the labor market for automobile workers is perfectly competitive (firms take output and input prices as given). is this enough information to calculate the marginal productivity of workers at the company? If not. what is the most that you can say about the marginal productivity of workers at GM given this information