Question

1. Karl's Cab Company has a monopoly in Junction City. The demand for taxi services in Junction City is given by Q = 5 – (1/6)P. KCC's costs are given by

TC = 14 + 3Q +3Q². Its profit maximizing output is

1. 1. .5
   2. 1.0
   3. 1.5
   4. 2.0
2. Karl's Cab Company has a monopoly in Junction City. The demand for taxi services in Junction City is given by Q = 5 – (1/6)P. KCC's costs are given by

TC = 14 + 3Q +3Q². Its maximum profits are

1. $1
2. $5
3. $6.25
4. $21
5. $14

Please show work.

Answer 1

Given, TC = 14 + 3Q + 3Q²

Marginal Cost (MC) = d(TC)/dQ = 3 + 6Q

Also, Q= 5 - (1/6)P

P = 30 - 6Q

Total Revenue (TR) = P*Q = (30 - 6Q) * Q = 30Q - 6Q²

Marginal revenue (MR) = d(TR) / dQ = 30 - 12Q

Profit maximizing condition for a monopoly is,

MC = MR

3 + 6Q = 30 - 12Q

18Q = 27

Q = 27/18 = 1.5 (c)

Therefore, profit maximizing output is 1.5

For this level of output,

Total Cost (TC) = 14 + 4.5 + 6.75 = $25.25

Total Revenue (TR) = 45 - 13.5 = $31.5

Therefore, maximum profit = TR - TC = $31.5 - $25.25 = $6.25 (c)