Question

Copy and paste the following data into Excel:

P Q

$87.50 370

$82.25 399

$81.38 410

$76.13 438

$70.88    444

a. Run OLS to determine the demand function as P = f(Q); how much confidence do you have in this estimated equation? Use algebra to invert the demand function to 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=$87.50? What is the point price elasticity of demand when P=$77.50?

d. To maximize total revenue, what would you recommend if the company was currently charging P=$82.25? If it was charging P=$77.50?

e. Use your first demand function to determine an equation for TR and MR as a function of Q, and create 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 = $87.50 and P = $77.50.

Answer 1

a) After running OlS, we get: P = 163.3984 – 0.20323Q

With 95% confidence, we can say that the estimated parameters are statistically significant.

On inverting; Q = 804.0072 + 4.9205P

b) e = (dQ/dP )*(P/Q), where: dQ/dP = 4.9205

Price	Quantity	e
87.5	370	1.1636
82.25	399	1.0143
81.38	410	0.9767
76.13	438	0.8552
70.88	444	0.7855

c) At P = $87.5, e = 1.636

At P =$77.5, Q = 1185.3485 and e = 0.3217

d) At P = $82.25, demand is elastic (e > 1). Thus, I would recommend the company to charge a lower price.

At P = $77.5, demand is inelastic (e < 1). Thus, I would recommend the company to charge a higher price.