Answer to Question #319934 in Microeconomics for souljaboy

Question

Use the production function Q = 10K^0.5 L^0.6  to complete the following production table

Rate of Capital Input(K)

 6 24.5 56.3 71.8

5

4 30.3

3 45.5

2 27.3

1 10.0 29.3

1 2 3 4 5 6

  Rate of Labour Input (L)

 

a) For this production system, are returns to scale decreasing, constant, or increasing? Explain.

b) Suppose the wage rate is $28, the price of capital also is $28 per unit, and the firm currently is producing 30.3 units of output per period using four units of capital and two units of labour.Is this an efficient resource combination? Explain. What would be a more efficient (not necessarily the best) combination? Why? (HINT: Compare the marginal products of capital and labour at the initial combination.)

Answer 1

b) $Q=10K^{0.5}L^{0.6}$

$w = 28, k = 28$ , $Q = 30.3 units, K = 4$ units, L = 2 units.

$MPL =\frac{ 6K^{0.5}}{L^{0.4}}$

$MPk =\frac{5L^{0.6}}{K^{0.5}}$

Marginal rate of technical substitution $MRTS = \frac{MPL}{MPk} = 2.4$

We need 2.4 units of K

for every unit of L.

So, K = 4 units and L = 2 units is not an efficient resource combination. A more efficient combination will be 4.8 units of K and 2

units of L.