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