Question #315458

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


1
Expert's answer
2022-03-23T16:23:38-0400

Q=10K0.5L0.6Q=10K^{0.5}L^{0.6}

w = $28,

k = $28, Q = 30.3 units,

K = 4 units, L = 2 units.

MPL = Q(L)=6K0.5/L0.4Q'(L) = 6K^{0.5}/L^{0.4}

MPk = Q(K)=5L0.6/K0.5Q'(K) = 5L^{0.6}/K^{0.5}

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

(6K0.5/L0.4)(5L0.6/K0.5)\frac {(6K^{0.5}/L^{0.4})}{( 5L^{0.6}/K^{0.5})} = 1.242\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.


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