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Good Morning Mr Moffat,
I hope you are well.
I was wondering if there is any chance that you may be able to help me with a question please? I have spent many hours trying to formulate the equation … but no luck. I think I am missing something very simple about b (change in price / change in quantity)…
Please can you point me in the right direction?
The question is as follows: The maximum demand for a product M is 100,000 units per annum. The demand will be reduced by 40 units for every increase of $1 in the selling price. The company has determined that profit is maximized at a sales volume of 42,000 units per annum. What is the profit maximizing price?
I am thinking P=a-bQ so
a-b*100,000=P – first equation
a-b*99,960=P+$1 – second equationand MR=MC=a-2bQ where Q(demand)=42,000.
I need value for b to solve this… or am I “barking at the wrong tree”?Any comments on this would be much appreciated.
Thanks a lot in advance.
Since the question tells you that the demand is 42,000 units for maximum profit, all you need to do is put 42,000 in the price demand equation to find out what the price is.
(You do not need to bother about MR = MC because they have already done that for you)
Maximum demand occurs when the SP is zero, and so: a = 100,000 / 40 = 2,500
So P = 2,500 – 1/40 Q, so when Q = 42,000 then P = 1,450
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