Economics 208 Fall Semester 2016 Assignment 2 Due: Wednesday, October 12 by noon, 2016 Note: No email pictures of assignment accepted. You can slip the assignment under my door or scan it and email it to me. Be sure to explain your answers. A grade of zero is applied to unexplained answers. 1. Given two prospects with the same expected value and with the help of a diagram, determine whether a risk-averse individual prefers the prospect with the smaller spread in the outcomes. Answer the same for a risk lover. 2. Clarence makes his choices by maximizing expected utility. Clarence is risk averse. (a) Clarence's friend Simon has offered to bet him $1000 on the outcome of the toss of a coin. If the coin comes up heads, Clarence must pay Simon $1000. If the coin comes up tails, Simon must pay Clarence $1000. If Clarence does not accept the bet, he will have $10,000 with certainty. Explain why Clarence refuses to take the bet. Illustrate this in a utility/wealth diagram. (b) Simon would like to entice Clarence to take the bet. If Clarence's utility function is given by U(x)=√x, what is the minimum amount that Simon must pay Clarence to take the bet? 3. Consider the following production function: . What is the average product of labour, holding capital fixed? What is the marginal product of labour? Determine whether the production function exhibits diminishing marginal productivity of labour. Determine the marginal rate of technical substitution. What returns to scale does the production function have? 4. A Montreal firm uses labour to produce a commodity according to a production function f(L)=4√L. The commodity sells for $P per unit and the nominal wage paid to workers is $W. (a) Determine the labour demand function from the profit maximization problem for the firm. Graph the labour demand function as a function of the real wage. (b) Suppose that currently the firm is employing 12 workers when the price of the commodity is $100 and the nominal wage paid to workers is $50. Should the firm hire more workers, less workers, or keep its labour input the same? (c) We can think of the number "4" in the production function as representing factors affecting the productivity of labour. Suppose that improvements in technology shift the production function. Show that this would shift the labour demand function as well. 5. A small firm produces a good using two inputs, labour ( ) and machines ( ). Her production function is . Suppose that the wage rate is $100 per hour and the price of a machine is $25 per unit. Suppose that the firm is currently employing a capital-labour ratio equal to 10. Is this the cost-minimizing capital-labour ratio? If it is, explain why it is. If it is not, explain what ratio the firm should employ. Illustrate the current position of the firm's production on a graph showing the isocost and isoquant and indicate where this current position is relative to the cost-minimizing position. Find the amounts of labour and capital that will produce 120 units at minimum cost. 6. Consider the following cost function: . What is the total variable cost function? What are the total fixed costs? What is the average variable cost function? What is the average fixed cost function? What is the average total cost function? What is the marginal cost function? For what level of output is average variable cost a minimum? What is the relationship between average and marginal cost?