Question

If the demand function is P = 70 - Q find an expression for TR in terms of Q.

(1) Differentiate TR with respect to Q to find a general expression for MR in terms of Q. Hence write

down the exact value of MR at Q = 60.

(2) Calculate the value of TR when

(a) Q=60 

(b) Q=61

and hence confirm that the 1 unit increase approach gives a reasonable approximation to the exact value of MR obtained in part (1).

Answer 1

1. TR(Q)=P(Q)Q=(70-Q)Q=70Q-Q²

$MR=TR(Q)'=70-2Q$

MR(60)=70-120=-50

2. $TR(60)=70\times60-3600=600$

$TR(61)=70\times61-3721=549$

549-600=-51