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?

Solution Preview

See attached Excel spreadsheet for full solutions.

Equation 1:
P = 20 - .2Q

TR = Q * P
P = 20 - .2Q
TR = Q * (20-.2Q)
TR = 20Q - .2Q^2

Take first derivative:
MR = 20 - ...

Solution Summary

A demand curve for haircuts are examined. The expert uses calculus to find the number of haircuts that maximize total revenues.

The demand curve for haircuts at Terry Bernard's Hair Design is P= 20-0.20Q where Q is the number of haircuts per week and P is the price of a haircut. ...

... 6. The demand curve for haircuts at Terry Bernard's Hair Design is: P=15-0.15Q where Q is the number of cuts per week and P is the price of a haircut. ...

... sequence of shifts in aggregate demand and supply curves A) Decrease ... rightward and does not shift the aggregate curve (C) aggregate demand curve leftward and ...

... 5 + e/4. All supplies and demands are denominated ... But barter is informationally demanding: we need n(n ... The aggregate demand curve is the same in both Keynesian ...

... are?---- 13) The following table shows demand ad marginal ... cost curve crosses its marginal revenue curve at an ... He charges $10 for a haircuts hair for 18 ...

... Assume that demand and marginal revenue curves for haircuts in ... expect hair cut price to be $20 (and consequently, 75000 haircuts will be demanded). ...

... the price level are determined by the SAS and demand curves. ... will lead to a decrease in domestic quantity demanded. ... d. If the demand for dollars decreases, the ...

... price barber knows the consumer's preferences in haircuts. ... at a different price Figure 1 Demand Curves with Shaded ... we have plot- ted the demand curve for total ...

... introducing new products or stimulating demand through advertising ... T he more powerful consumer demands a more ... with the diffusion of innovations curve, where we ...