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Finding the optimal price and output level

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The demand curve for tickets at an amusement park is:

Q = D(p) = 1400 - 46p, p > 0

The marginal cost of serving a customer is $11.

Using calculus and formulas (but no tables or spreadsheets) to find a solution, how many tickets will be sold at the profit-maximizing price?

Round the equilibrium quantity DOWN to its integer part and round the equilibrium price to the nearest cent.

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Solution Summary

Solution depicts the steps to find out the optimal price and output level in the given case.

Solution Preview

Q=1400-46p, p>0
On rearranging we get
46p=1400-Q
p=(1400/46)-(Q/46)
Total ...

Solution provided by:
Lokesh Jain, MSc
Education
  • BEng (Hons) , Birla Institute of Technology and Science, India
  • MSc (Hons) , Birla Institute of Technology and Science, India
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