Question

6. Given the following function TR(Q) -600Q -40 TC(Q) = 1000 + 10,200 a. b. c. d. e. Find the revenue maximizing level of output (check 2ad order conditions also), Find the maximum revenue Find the corresponding profit function Find the profit maximizing level of output (check 2nd order conditions also) Find the maximum profit

Answer 1

TR = 600Q- 4Q²

(a) To calculate revenue maximizing level of output , take the first order derivative of TR w.r.t Q and equate it to 0, we get:

600 - 2(4)Q = 0

600- 8Q =0

8Q= 600

Q= 75 units

And second order derivative w.r.t Q , we get:

-8 <0 (This implies that at Q=75 , TR reaches its maximum).

(b) At Q=75 , TR= 600(75) -4(75)²

= 45000- 22500 = $ 22500 (Maximum revenue)

(c) Profit = TR-TC

TP = 600Q - 4Q² -100Q -10,200

TP = 500Q -4Q² -10,200

(d) Take the first derivative of TP w.r.t Q and equate it to 0 , we get:

500 -8Q =0

8Q= 500

Q= 62.5 units

And second order derivative w.r.t Q ,

-8<0 (This means that at Q=62.5 ,TP reaches its maximum)

(e) At Q=62.5 , TP= 500(62.5)- 4(62.5)²-10,200

= 31250- 15625 -10200 = $ (31250- 25825 )= $ 5425 (Maximum profit)