The price that will maximize profits is $6.
At a price of $6, the quantity demanded will be 400,000 CDs.
The maximum profit will be $2,400,000, which is obtained by selling 400,000 CDs at a price of $6 each and incurring a fixed cost of $100,000 and a marginal cost of $800,000 (400,000 CDs x $2 per CD).
Suppose that Neptune Music has the copyright to the latest CD of the heavy Iron Band. The market demand schedule for the CD is:
Q = 800 – 100P.
Q represents quantity demanded measured in thousands of CDs and P represents the price in dollars. Production requires a fixed cost of $100,000 and a constant marginal cost of $2 per CD produced.
1.What price will maximize profits?
2.At the price you found in 1 above, how many CDs will be sold?
3.What is the maximum profit for the quantity and price you found above? level be in this case?
Here the function is demand Q=800-200P
Therefore,TR=PQ=800P-200P^2
MR=d(PQ)=800-2*200*P=800-400P
Here MC=2
Hence 800-400P=2
or -400P=-800+2=-798
or P=798/400=1.998
Again,Q=800-200P=800-200*1.995=389
Here Total cost(TC)=1000000+2*Q
Total Profit=TR-TC
Here the function is demand Q=800-200P
Therefore,TR=PQ=800P-200P^2
MR=d(PQ)=800-2*200*P=800-400P
Here MC=2
Hence 800-400P=2
or -400P=-800+2=-798
or P=798/400=1.998
Again,Q=800-200P=800-200*1.995=389
Here Total cost(TC)=1000000+2*Q(Most probably there is some mistake in the figure of total fixed cost)
Total Profit=TR-TC
1 answer