Question

Use the production function Q=10K0.5 L0. 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

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

Answer 1

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

w = $28,

k = $28, Q = 30.3 units,

K = 4 units, L = 2 units.

MPL = $Q'(L) = 6K^{0.5}/L^{0.4}$

MPk = $Q'(K) = 5L^{0.6}/K^{0.5}$

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

$\frac {(6K^{0.5}/L^{0.4})}{( 5L^{0.6}/K^{0.5})}$ = $\frac{1.2*4}{2}$ = 2.4

so 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.