# Demand & Marginal Revenue: Solve For Output to Maximize Profit

The demand curve for haircuts at Terry Bernard's Hair Design is P = 20 - 0.2Q, where Q is the number of cuts per week.

a. Should Terry raise the price of haircuts above its current $15 if he wants to increase revenue? Why or why not?

b. Use calculus to find the number of haircuts that maximizes total revenue. What price would Terry have to charge to reach this level of output? How much total revenue would be earned?

c. Suppose demand for Terry's haircuts increases to P = 40 - 0.4Q. At a price of $15, should Terry raise the price of her haircuts? Why or why not?

d. Again, use calculus to find the number of haircuts that maximizes total revenue given this new demand. What price would Terry have to charge to reach this level of output? How much total revenue is earned now?

e. Using the two equations for demand, determine equations for MR as a function of Q. Do two graphs, one of P and MR for the P = 20 - 0.2Q demand, and one of P and MR for the P = 40 - 0.4Q demand. Do the graphs confirm your answers to parts b and d? Why or why not?

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