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In: Economics

A firm has the following production function: q=KL The firm will produce 64 units of output...

A firm has the following production function: q=KL The firm will produce 64 units of output and faces prices for labor and capital of $4 and $1 respectively. What is the optimal quantity of labor and capital the firm should employ in order to minimize the cost of producing 64 units of output? What is the minimum cost of producing 64 units of output? Show the firms optimal production decision on a graph.

Solutions

Expert Solution

Production function : q = KL

q = 64 units .

w = 4$

r = 1$

Firm's cost minimization condition :

Tangency point between isocost and isoquant : MRTS = MPL / MPK = w / r

So , MPL = = K

MPK = = L

MPL / MPK = w / r

or , K/L = 4/1

or , K = 4L

q = KL = 4L2

( q= 64 ) L = 4 units . K = 16 units

Minimum cost or total cost = wL + rK = 16 + 16 = 32 $

Rahul Sunny answered 2 years ago
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