Exam 11: One Input and One Output: a Short-Run Producer Model

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If income effects are sufficiently strong, it may be the case that labor demand curves slope up.

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In the one-input model, the marginal product of labor curve falls below the horizontal axis only if the production frontier slopes down.

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For price-taking producers, isoprofit curves are always parallel to one another.

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In the one-input model of production, increasing marginal product implies non-convexity of the producer choice set.

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Labor demand curves are homogeneous of degree zero.

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Labor demand curves always slope down.

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Suppose a price-taking firm uses a single input - labor - to produce an output x.The production technology has diminishing marginal product of labor throughout. a.On a graph with labor hours on the horizontal and output on the vertical axis, illustrate the production frontier for this firm. b.For a given wage rate w and output price p, illustrate three isoprofit curves corresponding to profit levels π < π'< π" -- indicating slopes and intercepts.Suppose the profit maximizing plan results in profit π'.Then use isoprofit to illustrate the profit maximizing production plan for the firm and show how w and p are related to the marginal product of labor at that plan. c.Where on your graph do all cost-minimizing production plans lie? d.On a graph with output on the horizontal and dollars on the vertical axis, illustrate the shape of the cost curve for the firm (holding fixed w).Then suppose that, in addition to labor costs, the firm has to pay a recurring (long run) fixed cost F.Where does the long run cost curve lie in relation to the initial (short run) cost curve you drew? e.On a separate graph, illustrate the short run marginal and average cost curves.Then, on the same graph illustrate the long run marginal and average cost curves in the presence of the recurring fixed cost.f.Indicate where in your graph you can locate the short and long run supply curves for this firm.

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Suppose a single-input production function has initially increasing but eventually decreasing marginal product -- and suppose we know that an interior solution is profit maximizing.In this case, the first order condition for the profit maximization problem

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With all other inputs held fixed, the marginal product of any input must eventually increase as more of that input is hired.

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Price taking producers make zero economic profit when price falls

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In the one-input model, the cost curve is the inverse of the production frontier if and only if the input price is 1.

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Suppose you solve the profit maximization problem for a single-input, price-taking producer whose technology is given by Suppose you solve the profit maximization problem for a single-input, price-taking producer whose technology is given by   The labor demand function is    a.Suppose   Might   in fact be the correct labor demand function? Explain.  b.Suppose   Might   in fact be the correct labor demand function? Explain.  c.Intuitively explain how (b) might arise from the profit maximization problem. The labor demand function is Suppose you solve the profit maximization problem for a single-input, price-taking producer whose technology is given by   The labor demand function is    a.Suppose   Might   in fact be the correct labor demand function? Explain.  b.Suppose   Might   in fact be the correct labor demand function? Explain.  c.Intuitively explain how (b) might arise from the profit maximization problem. a.Suppose Suppose you solve the profit maximization problem for a single-input, price-taking producer whose technology is given by   The labor demand function is    a.Suppose   Might   in fact be the correct labor demand function? Explain.  b.Suppose   Might   in fact be the correct labor demand function? Explain.  c.Intuitively explain how (b) might arise from the profit maximization problem. Might Suppose you solve the profit maximization problem for a single-input, price-taking producer whose technology is given by   The labor demand function is    a.Suppose   Might   in fact be the correct labor demand function? Explain.  b.Suppose   Might   in fact be the correct labor demand function? Explain.  c.Intuitively explain how (b) might arise from the profit maximization problem. in fact be the correct labor demand function? Explain. b.Suppose Suppose you solve the profit maximization problem for a single-input, price-taking producer whose technology is given by   The labor demand function is    a.Suppose   Might   in fact be the correct labor demand function? Explain.  b.Suppose   Might   in fact be the correct labor demand function? Explain.  c.Intuitively explain how (b) might arise from the profit maximization problem. Might Suppose you solve the profit maximization problem for a single-input, price-taking producer whose technology is given by   The labor demand function is    a.Suppose   Might   in fact be the correct labor demand function? Explain.  b.Suppose   Might   in fact be the correct labor demand function? Explain.  c.Intuitively explain how (b) might arise from the profit maximization problem. in fact be the correct labor demand function? Explain. c.Intuitively explain how (b) might arise from the profit maximization problem.

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Since the marginal product of labor can increase initially as I hire more workers, demand for labor is also upward sloping for the initial workers I hire.

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Every profit-maximizing producer is cost minimizing.

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