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

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In the one-input model, a convex producer choice set implies an upward sloping marginal cost curve.

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The output level is constant along any isoprofit line.

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Price-taking producers have horizontal marginal revenue curves.

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When single-input producer choice sets are non-convex, the first order condition of the profit maximization problem is neither necessary nor sufficient for identifying the profit maximizing production plan.

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An increase in the wage will cause the output supply curve in the one-input model to shift in unless labor is an inferior input.

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Every cost-minimizing producer is profit-maximizing.

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Which of the following may be consistent with profit-maximizing behavior by a price-taking producer:

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Whenever average cost is increasing, marginal cost must also be increasing.

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In the one-input model, profit is always maximized where marginal revenue product is equal to the input price.

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If the single-input producer choice set is fully convex, the first order conditions of the profit maximization problem are necessary but not sufficient for identifying the profit maximizing production plan.

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A competitive (price-taking) firm will produce so long as its economic profit is sufficiently above zero to enable the firm to pay the owners of the firm for their time and effort.

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In the one-input model, a decrease in output price will always cause labor demand to shift in.

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Calvin buys newspapers and delivers them (by bike) to his customers' houses while Hobbes sells lemonade at his lemonade stand.One day they compare notes and find that Calvin, after paying for the newspapers and the maintenance on his bike, clears $5 per hour while Hobbes, after paying for the lemonade ingredients and upkeep of his lemonade stand, clears $4.50 per hour.The newspaper and lemonade businesses are the only possible trades for Calvin and Hobbes. a.If Calvin and Hobbes are identical, how much economic profit (per hour) is each making? b.Suppose Hobbes is slower on his bike than Calvin -- and he could only deliver half as many newspapers per hour.What's his economic profit in the lemonade business?

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If the single-input producer choice set is convex, the marginal product of labor curve must have a negative slope that is getting steeper with increases in labor input.

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The law of diminishing marginal product holds so long as the input is not a Giffen good.

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Suppose a technology is described by the production function Suppose a technology is described by the production function    a.For a price taking producer who faces output price p and wage w, derive the first order condition and interpret it. b.Without knowing more about the function f, is the condition you derived in (a) either necessary or sufficient for deriving the profit maximizing production plan? Explain. c.Suppose   .Derive the first order condition you illustrated in (a) and solve for   .  d.For what values of   is this first order condition necessary and sufficient for deriving a profit maximizing production plan? Explain. a.For a price taking producer who faces output price p and wage w, derive the first order condition and interpret it. b.Without knowing more about the function f, is the condition you derived in (a) either necessary or sufficient for deriving the profit maximizing production plan? Explain. c.Suppose Suppose a technology is described by the production function    a.For a price taking producer who faces output price p and wage w, derive the first order condition and interpret it. b.Without knowing more about the function f, is the condition you derived in (a) either necessary or sufficient for deriving the profit maximizing production plan? Explain. c.Suppose   .Derive the first order condition you illustrated in (a) and solve for   .  d.For what values of   is this first order condition necessary and sufficient for deriving a profit maximizing production plan? Explain. .Derive the first order condition you illustrated in (a) and solve for Suppose a technology is described by the production function    a.For a price taking producer who faces output price p and wage w, derive the first order condition and interpret it. b.Without knowing more about the function f, is the condition you derived in (a) either necessary or sufficient for deriving the profit maximizing production plan? Explain. c.Suppose   .Derive the first order condition you illustrated in (a) and solve for   .  d.For what values of   is this first order condition necessary and sufficient for deriving a profit maximizing production plan? Explain. . d.For what values of Suppose a technology is described by the production function    a.For a price taking producer who faces output price p and wage w, derive the first order condition and interpret it. b.Without knowing more about the function f, is the condition you derived in (a) either necessary or sufficient for deriving the profit maximizing production plan? Explain. c.Suppose   .Derive the first order condition you illustrated in (a) and solve for   .  d.For what values of   is this first order condition necessary and sufficient for deriving a profit maximizing production plan? Explain. is this first order condition necessary and sufficient for deriving a profit maximizing production plan? Explain.

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Output supply curves always slope up in the one-input model.

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Suppose a single-input production function has initially increasing but eventually decreasing marginal product.In this case, the first order condition for the profit maximization problem

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If profit from producing would be negative, producers will shut down.

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In the one-input model, the marginal cost curve is U-shaped.

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