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.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 create graph of P and MR on the vertical and Q on the horizontal axis.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.
Bob's Underground, a limited liability corporation specializing in new rap artists (B.U. LLC, rap) has the following demand function:
where Q is the quantity demanded of the most popular product B.U. sells, P is the price of that product, M is income, and PR is the price of a related product. The regression results are:
Adjusted R Square
0.8222
Independent Variables
Coefficients
Standard Error
t Stat
P-value
Intercept
-32.32
65.77
-0.491
0.626
P
-2.46
1.38
-1.813
0.079
M
0.008
0.001
6.045
9.53E-07
PR
-2.56
1.26
-2.025
0.051
a. Discuss whether you think these regression results will generate good sales estimates for B.U. LLC, rap.
Now assume that the income is $35,000, the price of the related good is $24, and B.U. chooses to set the price of its product at $21.
b. What is the estimated number of units sold given the data above?
c. What are the values for the own-price, income, and cross-price elasticities?
d. If P increases by 4%, what would happen (in percentage terms) to quantity demanded?
e. If M increases by 3%, what would happen (in percentage terms) to quantity demanded?
f. If PR decreases by 5%, what would happen (in percentage terms) to quantity demanded?
2.