Copy and paste the following data into Excel:
P. Q
$4.80 1170
$4.53 1235
$3.98 1337
$3.72 1442
$3.49 1548
a. Run OLS 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=$3.98? What is the point price elasticity of demand when P=$3.81?
d. To maximize total revenue, what would you recommend if the company was currently charging P=$4.53? If it was charging P=$3.81?
e. Use your indirect demand function to determine an equation for TR and MR as a function of Q, and make a graph of P and MR on the vertical and Q on the horizontal axis.
f. What is the total-revenue maximizing price and quantity, and how much revenue is earned there? Compare that to the TR when P = $4.80 and P = $3.81.