Question

A firm has the revenue function R = 600q - 0.03q² and the cost function is C = 150_q + 60,000, where q is the number of units produced. Find AR, AC, MR, and MC.

Answer 1

Given:
R = 600q – 0.03q²
C = 150q + 60000

1. AR = \(\frac { R }{ q }\)
   = \(\frac{600 q-0.03 q^{2}}{q}\)
   = \(\frac { 600q }{ q }\) – \(\frac{0.03 \mathrm{q}^{2}}{\mathrm{q}}\)
   = AR = 600 – 0.0.q
2. AC = \(\frac { c }{ q }\)
   = \(\frac { 150q + 60000 }{ q }\)
   = \(\frac { 150q }{ q }\) + \(\frac { 60000 }{ q }\)
   AC = 150 + (\(\frac { 60000 }{ q }\))
3. MR = \(\frac { dr }{ dq }\)
   R = 600q – 0.03q
   \(\frac { dR }{ dq }\) = 600 (1) – 0.03 (2q)
   MR = 600 – 0.06q
4. MC = \(\frac { dc }{ dq }\)
   C = 150q + 60000
   \(\frac { dc }{ dq }\) = 150 (1) + 0
   MC = 150