Question

For the following total revenue and total cost functions of a firm:

TR = 22Q-0.5Q²

TC = 1/3 Q³ - 8.5Q² + 50Q+90

.

a) Determine the level of output at which the firm maximizes its total profit.

b) Determine the maximum profit that the firm could earn.

Answer 1

a) The total revenue function is

TR= 22Q-0.5Q²

therefore, marginal revenue function is

MR= d(TR)/dq = 22-2*0.5Q= 22-Q (Taking first order derivative of total revenue function with respect to Q)

Again total cost function is

TC= 1/3Q³ -8.5Q² +50Q +90

Therefore, marginal cost function is

MC = Q² -17Q +50

Under profit maximization condition of a firm,

                       MR= MC

     i.e., 22-Q= Q² -17Q +50

     or, Q² -16Q+28=0

   or, (Q-14)(Q-2)=0 or, Q=14 and Q=2

For Q=14,

TR= 22*14-0.5*14² = 210

Again for Q=2,

TR = 22*2-0.5*2² = 42

Therefore, profit maximizing output of a firm is 210

b) The maximum profit of a firm = TR-TC= 210-(1/3*14³ -8.5*14² +50*14+90)= 171.33

answered by: anonymous