Question

A production process requires 4 units of labor (L) and 12 units of capital (K) to...

A production process requires 4 units of labor (L) and 12 units of capital (K) to produce one unit of output. The markets for labor and capital are NOT perfectly competitive. Furthermore, the markets for labor and capital experience common shocks, so =.75. The cost of a unit of labor is normally distributed with a mean of $20 and a standard deviation of $2. The cost for a unit of capital is normally distributed with a mean of $30 and a standard deviation of $1.

What is the variance of the cost to produce one unit of output?  

Math   Statistics-And-Probability   
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Answer #1

ANSWER::

Corr( L, K) = 0.75

Cov(L, K) = SD(L)* SD(K)*0.75

= 2*1*0.75

= 3/2

V( the cost to produce one unit of output) = V(4L + 12K) = V(4L) + V(12K) + 2*Cov(4L, 12K)

= 16*V(L) + 144*V(K) +2*4*12Cov(L, K)

= 16*4 + 144*1+ 2*4*12*3/2

= 64 + 144 + 144

=352

variance of the cost to produce one unit of output = 352

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