Question

Suppose the production function for automobiles is ? = ?? where Q is the quantity of automobiles produced per year, L is the quantity of labor (man-hours) and K is the quantity of capital (machine hours).

a) What is the total product (number of automobiles) if the firm uses 25 man hours and 2 machine hours?

b) Sketch the isoquant corresponding to a quantity of Q=50.

c) What is the general equation for the isoquant corresponding to any level of output Q (i.e. K in terms of L and Q)?

d) Find the general formula for the marginal rate of technical substitution of labor for capital for this production function.

e) Does the isoquant exhibit a diminishing marginal rate of technical substitution?

Answer 1

Q.

a.

We have:

Q = LK

With L = 25 and K = 2, we have:

Total product = Q = 25 x 2 = 50.

b.

Isoquant corresponding to Q = 50,

KL = 50

c.

General equation for isoquant for total product = Q,

KL = Q

d.

General formula for MRTS:

e.

Yes.

As we go down the isoquant towards increasing levels of L and reducing K, value of MRTS decreases.

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