Question

I'd like to know how to solve this micro economic question

This is True and False question

Given the short run production function q= 20L^2 - L^3, and a wage of $10, when L=10 marginal cost is $0.10.

Answer 1

Given, q = 20L^2 – L^3

If (L = 10), q would be as below

q = 20×10^2 – 10^3

   = 20 × 100 – 1,000

   = 2,000 – 1,000

   = 1,000

TC at 1,000 units of production = L × w

TC at 1,000 units of production = 10 × $10 = $100

Now, if the q is 1 unit less than 1,000 then,

q = 20L^2 – L^3

(1,000 – 1) = 20L^2 – L^3

999 = 20L^2 – L^3 …. (1)

Now if we take (L = 9.99) the equation (1) is satisfied. (It is done through trial and error method).

Therefore, for 999 units of production the requirement of L is 9.99.

TC at 999 units of production = L × w

TC at 999 units of production = 9.99 × $10 = $99.90

MC = TC at 1,000 units of production - TC at 999 units of production

       = $100 - $99.90

       = $0.10

Answer: True