Question

5.         You are provided with a pair of demand and cost functions.

            P = 20,000 - 15.6 Q                 TC = 400,000 + 4640 Q + 10 Q²

            Use the above functions and derive the maximum profits for the firm:

Optimal Q =

Optimal P =

Optimal TR =

Optimal profits =

6.         Calculate the break-even output level for the TC function given below. Also check whether MC = ACat this level.

                                                TC = 5 Q² + 10 Q + 125                    

Optimal Q =

Optimal AC =

Optimal MC =

7.         Calculate the shut-down output level for the TC function given below. Also check whether MC = AVC at this level.

                                                TC = 100 + 17 Q - 8 Q² + Q³

Optimal Q =

Optimal AVC =

Optimal MC =

Answer 1

Answer 5 : P= 20,000-15.6Q

TR = P* Q = (20,000-15.6Q)*Q = 20,000Q-15.6Q²

MR= 20,000-31.2Q

TC = 40,000+4640Q+10Q²

MC = 4640+20Q

Optiumal Q

MR= MC

20,000-31.2Q= 4640+20Q

20,000-4640 = 31.2Q+20Q

15,360= 51.2Q

15,360/51.2 = Q

Q= 300 units

Optiumal Q= 300 units

Optiumal P = 20,000-15.6*300 = 15,320

Optiumal TR = P*Q = 15,320*300= 4596000   

Optiumal TC = 40,000+4640*300+10*300*300

= 2,33,2000

Answer 6 : TC = 5Q²+10Q+125

AC = 5Q+10+125/Q

MC = 10Q+10

AC = MC ( Break even point)

5Q+10+125/Q= 10Q+10

5Q+10+125/Q-10Q-10=0

Q= 5 units

Optiumal Q = 5 units

Optiumal MC = 10*5+10 = 60 units

Optiumal AC = 5*5+10+125/5 = 60 unit

Answer 7 : Shut down output level

TC = 100+17Q-8Q²+Q ³

MC = 17-16Q+3Q²

VC = 17Q-8Q²+Q ³

AVC = 17-16Q+3Q²

MC = AVC ( Shut down point)

17-16Q+3Q²= 17-8Q-Q²

Optiumal Q= 4 units

Optiumal MC = 1

Optiumal AVC = 1( put value of Q = 4 units in AVC derived above)