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).

Here the follow table shows the result of OLS estimation.

So, here the estimated regression equation is given by, => P = 163.39 - 0.20*Q”. Now, the “p-value” of the “F” statistic is “0.0072 < 0.01”, => we have “more than 99%” confidence in this estimated equation.

=> P = 163.39 – 0.20*Q, => 0.20*Q = 163.39 – P, => Q = 163.39/0.2 – P/0.2.

=> Q = 816.95 – 5*P, the quantity demanded in terms of “P”.

B).

Here the demand curve is “Q = 816.95 – 5*P”, => dQ/dP = (-5). The following table shows the elasticity for the different combinations of “P” and “Q”.

C).

The point elasticity of demand for “P=87.5” is “(-1.18)”. Now, given the demand curve the quantity demanded for “P=77.5” is given by.

=> Q = 816.95 – 5*P, => Q = 816.95 – 5*77.5, => Q = 429.45. So the point elasticity of demand for “P=87.5” is “(-5)*(77.5/429.45) = (-0.90)”.

D).

At price “P=82.25” the absolute value of elasticity is “(1.03) > 1”, => at this point the demand is elastic, => the firm should reduce price to maximize revenue. Now, for “P=77.5” the absolute value of elasticity is “0.9 < 1”, => at this point the demand is inelastic, => the firm should increase price to maximize revenue.