Question

1. Suppose a firm’s production function is given by Q = K(1/3)L(2/3), whereMPK = 1K(−2/3)L(2/3) and MPL = 2K(1/3)L(−1/3)

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1. (a) What happens to MPK as K increases? Hint: consider how MPK changes as Kchanges by one unit at low values of K high levels of K. (2 points)

2. (b) What happens to MPK as L increases? (2 points)

3. (c) Explain why MPK changes as L changes. (3 points)

Answer 1

Differentiating Q wrt L we get

Similarly,

Let us assume K = 8, L =8

Therefore, Q = 8

A. When K increases then the value of MP_K will decrease.

When K =8 and L = 8

Now, assume K increases to 9

So, as K increases the value of MP_K decreases.

B. Assume K = 8 and L=8

Then

MP_K = 0.33

Now assume K = 8, L = 27

MP_K = 0.75

So, the value of MPk increases with the increase in L.

C. When L changes then the value of MP_K changes because the Marginal product of capital contains Labour too. Since, it is in the numerator so as L will increase so MPK will increase.

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