Question

3. The White Noise Corporation has estimated the following Cobb-Douglas production function using monthly observations for the past two years:

ln Q = 1.386 + 0.20 ln K + 0.30 ln L + 0.25 ln N

where Q is the number of units of output, K is the number of units of capital, L is the number of unit of labor, and N is the number of units of raw materials. With respect to the above results, answer the following questions when K = 400, L = 800 and N =200.

a. Q

b. Rewrite the estimated function in the form of a power function

. c. Find the marginal products of capital, labor, and raw materials

d. Find the value of the output elasticities of K, L, and N

e. Determine whether the returns to scale are increasing, decreasing or constant

f. Suppose the price of capital is $5.25 per unit, the price of labor is $7, and price of raw materials is $17.50 per unit. This this an optimal combination of resources

g. What price would the company have to charge for the product to maximize profits (25 points)

Answer 1

Due to presence of HOMEWORKLIB POLICY, I am answering first 4 parts.

a.

We have:

ln Q = 1.386 + 0.20 ln K + 0.30 ln L + 0.25 ln N

which can be also written as:

Removing logarithm, we get:

Using values: K = 400, L = 800 and N =200, we have:

b.

We have:

ln Q = 1.386 + 0.20 ln K + 0.30 ln L + 0.25 ln N

which can be also written as:

Removing logarithm, we get:

c.

Marginal products:

Using values, we get:

Using values, we get:

Using values, we get:

d.

Elasticities:

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