Copy and paste the following data into Excel:
 P         Q
$130    78
$110    155
$90      246
$70      318
$50      397

a. Run Regression to determine the inverse demand function (P = f(Q)); how much confidence do you have in this estimated equation? Use algebra to then find the direct demand function (Q = f(P)).

b. Using calculus to determine dQ/dP, construct a column which calculates the point-price elasticity for each (P,Q) combination.

c. What is the point price elasticity of demand when P=$90?What is the point price elasticity of demand when P=$83?

d. To maximize total revenue, what would you recommend if the company was currently charging P=$83? If it was charging P=$70?

e. Determine an equation for MR as a function of Q, and create a graph of P and MR on the vertical and Q on the horizontal axis.

f. Use your direct demand function to construct an equation and column for TR. What is the total-revenue maximizing price and quantity, and how much revenue is earned there? Compare that to the TR when P = $83 and P = $70.