Determine if the following statements are true or false. A. Suppose for a particular production function...

Determine if the following statements are true or false.

A. Suppose for a particular production function that MPL = 36(K/L) and MPK = 36(L/K) The price of capital is $5 per unit and the price of labor is $125 per unit. At the cost-minimizing combination of capital and labor, the firm should employ five times as much capital as labor.

B. The lower is the elasticity of substitution between capital and labor, the more inelastic labor demand will be.

C. The short-run total cost of producing some level of output can never be lower than long-run total cost.

D. Suppose in a particular production process that capital and labor are perfect substitutes so that three units of labor can always be substituted for one unit of capital. If the price of capital is $4 per unit and the price of labor is $1 per unit, the firm should employ only capital to minimize the cost of producing its output level.

Solutions

Expert Solution

A. At cost minimising combination : MPL/MPK = w/r

Here MPL = 36(K/L)

And MPK = 36(L/K)

w= $125

r = $5

MPL/MPK =w/r

[36(K/L) / 36(L/K)] = 125/5

K²/ L² =25

K/L =5

K = 5L

Hence, it implies that at cost minimising combination of capital and labor , the firm should employ five times as much times as much capital as labor. Hence, the given statement is TRUE.

(B) TRUE, the lower the elasticity of substitution between capital and labor , the more inelastic labor demand will be . Because firm is more willing to pay higher labor costs ,if it is not easy for the firms to substitute capital for labor.

(C) TRUE, the short run total costs of producing some level of output can never be lower than long run total cost because long run is the minimum possible cost for producing the given level of output among the short run costs.So, short run cpsts can never be lower than long run costs.

(D) FALSE , because capital and labor are perfect substitutes and three units of labor can always be substituted for one unit of capital. It implies MRTS= 1/3. And price of capital = $4 per unit and price of labor = $1 per unit. It implies w/r = 1/4 .

Because w/r < MRTS . It implies that the firm should employ only labor to minimize the cost of producing its output level.

Rahul Sunny answered 1 year ago

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