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Lectures in Microeconomics-Charles W. Upton Properties of Cost Functions C = C(q,r,w)

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Properties of Cost Functions General Cost Function C = C(q,r,w)

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Properties of Cost Functions General Cost Function C = C( q,r,w) The higher the value of q, the greater the total cost of production

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Properties of Cost Functions General Cost Function C = C(q, r, w ) The higher the value of q, the greater the total cost of production Ditto for r and w

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Properties of Cost Functions General Cost Function C = C(q,r,w) I illustrate the problems with seven trick questions

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Properties of Cost Functions First Trick Question Acme Widgets’ costs are now $100. It doubles output.

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Properties of Cost Functions First Trick Question Acme Widgets’ costs are now $100. It doubles output. Will costs double?

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Properties of Cost Functions First Trick Question Acme Widgets’ costs are now $100. It doubles output. Will costs double? They will surely go up but may or may not double.

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Properties of Cost Functions First Trick Question Acme Widgets’ costs are now $100. It doubles output. Will costs double? They will surely go up but may or may not double. Constant returns to scale ( C= $200) Increasing returns to scale ($100

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Properties of Cost Functions Second Trick Question Acme Widgets’ costs are now $100; $50 of (factor) payments to workers and $50 of payments to capital.

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Properties of Cost Functions Second Trick Question Acme Widgets’ costs are now $100; $50 of (factor) payments to workers and $50 of payments to capital. If wage rates increase by 100%, will total costs go from $100 to $150?

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Properties of Cost Functions Second Trick Question Acme Widgets’ costs are now $100; $50 of (factor) payments to workers and $50 of payments to capital. $100 K L

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Properties of Cost Functions Second Trick Question Acme Widgets’ costs are now $100; $50 of (factor) payments to workers and $50 of payments to capital. $100 K L $150

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Properties of Cost Functions Second Trick Question Acme Widgets’ costs are now $100; $50 of (factor) payments to workers and $50 of payments to capital. $100 K L $150 Substitute!

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Properties of Cost Functions Second Trick Question Acme Widgets’ costs are now $100; $50 of (factor) payments to workers and $50 of payments to capital. $100 K L $150 Substitute! If wage rates increase by 100%, will total costs go from $100 to $150? No!

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Properties of Cost Functions Third Trick Question Is it possible that higher wage rates will to enough substitution to lower total costs for the given level of output?

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Properties of Cost Functions Third Trick Question Is it possible that higher wage rates will to enough substitution to lower total costs for the given level of output? Assume a new solution of –$60 of capital payments and $30 of labor costs

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Properties of Cost Functions Third Trick Question Is it possible that higher wage rates will to enough substitution to lower total costs for the given level of output? Assume a new solution of –$60 of capital payments and $30 of labor costs At the old wage rate –$60 of capital payments and $15 of labor costs

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Properties of Cost Functions Third Trick Question Is it possible that higher wage rates will to enough substitution to lower total costs for the given level of output? Assume a new solution of –$60 of capital payments and $30 of labor costs At the old wage rate –$60 of capital payments and $15 of labor costs No! This could happen only if Acme were overpaying in the first place.

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Properties of Cost Functions End ©2004 Charles W. Upton

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