1.Copy and paste the following data into Excel:

P

Q

$374.00

8320

$370.26

8743

$351.56

9083

$347.82

9503

$332.86

9690

$310.42

10087

$306.68

10240

$299.20

10641

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=$374.00? What is the point price elasticity of demand when P=$324.50?

d.To maximize total revenue, what would you recommend if the company was currently charging P=$351.56? If it was charging P=$324.50?

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? (Round your price to the nearest cent, your quantity to the nearest whole unit, and your TR to the nearest dollar.) Compare that to the TR when P = $374.00 and P = $324.50.

2.Your company, which specializes in equipment for the popular activity combining equine sports and ice hockey (HorsePuckey), has the following demand function:

Q = a + bP + cM + dR

where Q is the quantity demanded of HorsePuckey hockey pucks, P is the price of that product, M is consumer income, and R is the price of a related product.The regression results are:

Adjusted R Square

0.6883

Independent Variables

Coefficients

Standard Error

t Stat

P-value

Intercept

9975.02

97.02

102.81

6.64E-42

P

-8.537

3.193

-2.674

0.012

M

0.0058

0.002

3.812

0.001

R

-3.65

1.427

-2.556

0.016

a.Discuss whether you think these regression results will generate good sales estimates for HorsePuckey.

Now assume that the income is $58,952, the price of the related good is $13.50, and HorsePuckey chooses to set the price of its product at $6.38.

b.What is the estimated number of units sold given the data above? (round to nearest unit; no decimals)

c.What are the values for the own-price, income, and cross-price elasticities?

d.If P increases by 8%, what would happen (in percentage terms) to quantity demanded?

e.If M decreases by 2%, what would happen (in percentage terms) to quantity demanded?

f.If R increases by 3%, what would happen (in percentage terms) to quantity demanded?