3. (a) If the demand function is P = 60 – Q find an expression for TR in terms of Q. 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 = 50. Calculate the value of TR when (a) Q = 50 (b) Q = 51 and hence confirm that the 1 unit increase approach gives a reasonable approximation to the exact value of MR obtained in part (1) (b) The consumption function is C = 0.01Y2 + 0.8Y + 100 (i) Calculate the values of MPC and MPS when Y = 8. (ii) Use the fact that C + S = Y to obtain a formula for S in terms of Y. By differentiating this expression find the value of MPS at Y = 8 and verify that this agrees with your answer to part (a).
3. (a) If the demand function is
P = 60 – Q
find an expression for TR in terms of Q.
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 = 50.
Calculate the value of TR when
(a) Q = 50 (b) Q = 51 and hence confirm that the 1 unit increase approach gives a reasonable approximation to the exact value of MR obtained in part (1)
(b) The consumption function is
C = 0.01Y2 + 0.8Y + 100
(i) Calculate the values of MPC and MPS when Y = 8.
(ii) Use the fact that C + S = Y to obtain a formula for S in terms of Y.
By differentiating this expression find the value of MPS at Y = 8 and verify that this agrees with your answer to part (a).
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