Exam 12: Production With Multiple Inputs

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All economically efficient production plans are technologically efficient.

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If producer choice sets are convex and a production plan satisfies the condition that the (marginal)technical rate of substitution is equal (in absolute value)to the ratio of input prices,then the production plan is profit maximizing.

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Assuming an interior solution,a production plan is profit maximizing if and only if all marginal revenue products are equal to input prices.

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Changing the labels on isoquants without changing the shapes of the isoquants implies no change in the underlying technology so long as the ordering of isoquants is preserved.

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Increasing returns to scale production technologies cannot give rise to convex producer choice sets.

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In one-input models,all technologically efficient production plans are economically efficient and vice versa.

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Suppose capital and labor are perfect complements in production.For output levels between 0 and 100,2 units of labor together with 1 unit of capital produce 1 unit of output; for output levels between 100 and 200,1 unit of labor together with 1 unit of capital produces 1 unit of output; and for output levels above 200,1 unit of labor together with two units of capital produces one additional output.In each graph below,carefully label as much of each graph as you can. a.On a graph with labor on the horizontal axis and capital on the vertical,illustrate isoquants for 100,200 and 300 units of output. b.Is this production technology homothetic? c.Suppose the wage and rental rates are 10.On a graph with output on the horizontal axis and dollars on the vertical,plot the total (long run)cost of producing 100,200 and 300 units of output and illustrate the total cost curve. d.On a separate graph with output on the horizontal and dollars on the vertical axis,illustrate the (long run)marginal cost curve and the approximate shape of the long run average cost curve.

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If production technologies are homothetic,all cost-minimizing production plans lie on the same ray from the origin for a given set of input prices.

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Just as indifference maps represent consumer tastes,so isoquant maps represent a producer tastes.

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Cobb-Douglas production function have decreasing returns to scale.

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