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Hi John
Sorry for this but just sat one the exam bank questions and really struggled to find answer.
Question is – sales price is $200. Demand at this price is 100,000 units. Demand will change by 10,000 for every $30 movement on price and variable costs are $8 per unit.My solution (incorrect as not even an option to answer was:
P = a – bq means p = 500 – 0.003q
MR = a – 2bq means 192 (being 200-8) = 500 – 0.006q; therefore 500-192 = 0.006q means q = 51333
Back to original equations
P = 500-0.003×51333
P = 500 – 154.
P = 346.The correct answer is $254 and I just can’t fathom how to get there.
Your help would be much appreciated.
Kind Regards
Chris
Hi Chris
You started correctly, but then you went wrong 🙂
P = 500 – 0.003Q That is correct
Therefore MR = 500 – 0.006Q
MC = 8 (the variable cost per unit)So for maximum profit, MR = MC
500 – 0.006Q = 8
0.006Q = 500 – 8 = 492
So Q = 492/0.006 = 82,000If you now put Q = 82,000 in the original price/demand equation, you will get P to be $254
I hope that all makes sense 🙂
It does – I’m an idiot! So close yet so far! I was using the MR as $192 rather than $8 as the MC. Silly boy! Getting my MR’s and contributions mixed up and ignoring the more obvious (and correct!) figures. Lesson learned and better now than in 2 months time!
PS – many thanks as always for your prompt response and assistance and clarity. Goes without saying that your support is invaluable (but I’ll say it anyway!).
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