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Dear Sir- I came across this Q in the BPP Revision kit (Q102) Page 28- on the profit maximisation SP.
It seems a very simple Q but unable to get the correct answer. I am struggling to understand the explanation given at the back of the book. I tried using the demand function and substituting values in the MR function but in vain I would appreciate if you could please help.
Thank you in advance..I think you must be using an old edition of the Revision Kit, because Q102 in the current edition is not asking about profit maximisation. It is asking about elasticity and is not requiring any calculations.
Ok. The question is as below-
Market research into demand for a product indicates that when the selling price per unit is $145, demand in each period will be 5000 units; if the price is $120 demand will be 11,250 units. It is assumed that the demand function for this product is linear. The variable cost per unit is $27.
What selling price should be charged in order to maximise the monthly profit?Thank you.
In the price demand equation:
b = (145 – 120) / (11,250 – 5,000) = 0.004
a = 145 + (5,000 x 0.004) = 165Therefore P = 165 – 0.004Q
Therefore MR = 165 – 0.008Q
For maximum profit, MR = MC
so 165 – 0.008Q = 27
0.008Q = 138
Q = 138 / 0.008 = 17,250Using this in the price demand equation gives:
P = 165 – (0.004 x 17,250) = $96
Have you watched my free lectures on this? The lectures are a complete free course for Paper PM and cover everything needed to be able to pass the exam well.
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