Question

Suppose that a firm has production function F(L, K) = L1/4 K3/4 for producing widgets, the wage rate for labor is w = $32, and the rental rate of capital is r = $6. Suppose the firm has an order to produce 40 units of output.

a) Carefully write out the firm’s cost minimization problem, using information specific to this problem.

b) Express two equations—specific to this problem—that the optimal solution satisfies.

c) Solve these two equations for L* and K*.

d) Determine the firm’s cost of meeting the order.

e) Resolve this problem, leaving the production goal Q as a variable in order to get the firm’s cost function C(Q).

Answer #1

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A production function for widgets is given by Q = f(L,K) =
L1/2 K1/2 where L and K denote,
respectively, the level of the homogeneous units of labour and
capital used in production.
a) If a producer wishes to produce 45 widgets and has hired 25
units of labour, how many units of capital must be used to fill
this order?
b) If a producer has received an order for 30 widgets which must
be produced but only has 9...

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Consider a firm with the production function
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Show your work

2. Suppose a firm is producing 200 widgets. The firm’s
production function is Cobb-
Douglas with decreasing returns to scale. (This means we have
normal, convex
isoquants). The firm uses K’ units of capital and L’ units of
labor. Initially, the input prices
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the wage rate, resulting in an increase in input prices from w’
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a graph (of isoquant...

Suppose a firm’s long-run production function is given by
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(rental rate denoted by r) is $1200 per machine-hour and the cost
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Hint: if you don’t calculate the
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4. Suppose a small oil drill has the following production
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(c) Setup the cost minimization problem where labor and capital are
flexible. Then find the cost function if...

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