2. Copy and paste the following data into Excel 4.80 1170 $4.531235 3.98 1337 S3

Question

2. Copy and paste the following data into Excel 4.80 1170 $4.531235 3.98 1337 S3.72 1442 $3.49 1548 a. Run OLS to determine the inverse demand function (P-fQ; how much confidence do you b. Using calculus to determine dQ/dP, construct a column which calculates the point-price elasticity c. What is the point price elasticity of demand when P-S3.98? What is the point price elasticity of d. To maximize total revenue, what would you recommend if the company was currently charging e. Use your indirect demand function to determine an equation for TR and MR as a function of Q f. What is the total-revenue maximizing price and quantity, and how much revenue is earned there? have in this estimated equation? Use algebra to then find the direct demand function (Q = f(P) for each (P.Q) combination. demand when P=$3.81? P=$453? If it was charging P=$3.81? and create a graph ofP and MR on the vertical and Q on the horizontal axis Compare that to the TR when P = $4.80 and P = $3.81

Explanation / Answer

a) P = 8.85-0.0035Q

Regression Statistics

Multiple R

0.982068

R Square

0.964458

Adjusted R Square

0.952611

Standard Error

0.119518

Observations

5

ANOVA

df

SS

MS

F

Significance F

Regression

1

1.162867

1.162867

81.40758

0.002875

Residual

3

0.042853

0.014284

Total

4

1.20572

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

8.854859

0.529256

16.73077

0.000465

7.17053

10.53919

7.17053

10.53919

X Variable 1

-0.00353

0.000391

-9.02261

0.002875

-0.00477

-0.00228

-0.00477

-0.00228

Confident at95% level of confidence since the value lies in the CI.

b)

P = 8.85-0.0035Q

dP/dQ = -0.0035

dQ/dP = -1/0.0035

dQ/dP = 285.71

Elasticity:

e= dQ/dP*(P/Q)

c) P = $3.98

TR = P*Q = 3.98*1337

=$5321.26

P = $3.81

At P = 3.81

3.81 = 8.85-0.0035Q

0.0035Q = 8.85-3.81

Q = 1440

TR = 3.81*1440

=$ 5486.4

d)

P = $4.53

Q = 1235

TR = 4.53*1235

=$5594.55

TR is maximized at P = $4.53

AT $3.81 Revenue can be increased by charging $4.53 instead.

Regression Statistics

Multiple R

0.982068

R Square

0.964458

Adjusted R Square

0.952611

Standard Error

0.119518

Observations

5

ANOVA

df

SS

MS

F

Significance F

Regression

1

1.162867

1.162867

81.40758

0.002875

Residual

3

0.042853

0.014284

Total

4

1.20572

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

8.854859

0.529256

16.73077

0.000465

7.17053

10.53919

7.17053

10.53919

X Variable 1

-0.00353

0.000391

-9.02261

0.002875

-0.00477

-0.00228

-0.00477

-0.00228

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