MEMO 14 Third-Degree Price Discrimination Firms can take advantage of the differences in consumersâ€™ demand in order to increase their profit. Price discrimination is the method by which this is accomplished. Price Discrimination means that the firm charges different prices for the same good. To practice price discrimination successfully, firms need knowledge of the distribution of consumersâ€™ willingness to pay.Certain conditions are necessary for the firm to be able to price-discriminate.

The firm must possess some market power

The demand functions for the individual consumers or groups of consumers must differ.

The different markets must be separable

Purchasers of the product must not be able to resell it to other customers.

The analysis of price discrimination is a straightforward application of the MR=MC rule.[2] The firm should equate the marginal revenue from selling output to each group to marginal cost.[3] MR1=MC MR2=MC And MR1 = MR2 The model of thirdâ€“degree monopolistic price discrimination, a monopolist is assumed to sell a homegeneouos product at different prices to market segments that do not overlap. The markets are assumed, therefore, to be perfectly scaled, that is consumers in one market are not allowed to purchase in the other markets.[4] A manager who wishes to maximize the total revenue in two separate markets should allocate sales between the two markets so that MR1 = MR2 and all units are sold. Although the marginal revenues in the two markets are equal, the prices are charged are not. The higher price will be charged in the market with the less elastic demand and the lower price will be charged in the market having the more elastic demand. In the more elastic market, price could be raised only at the expense of a large decrease in sales. In the less elastic market, higher prices bring less reduction in sales.[5] MR = P( 1+ 1/E) MR= Marginal Revenue P= Price E= Elasticity To maximize profit, a firm produces the output at which the marginal revenue to each group equals marginal costs. MR1= P1(1+1/E1)=MC MR2= P2 (1+1/E2)=MC And MR1= P1(1+1/E1) = MR2= P2 (1+1/E2) Since MR1 and MR2 must both be positive, E1 and E2 must both be greater (in absolute value) than one. P1 < P2 and |E1| >|E2| A manager who price-discriminates in two separate markets, will maximize total revenue by charging the lower price in more elastic market and the higher price in the less elastic market. Memo-14 Sports and Musics Firm offers two small program packages to whom using their basic package. The first is a sports package which includes NBA TV and the soccer Channel. The second is a music package that includes MTV2 and GAC. There are 2 markets; region 1 and region 2. The firm estimated that incremental cost for the sports package are $ 1.45 per subscriber and the incremental cost for the music package are $1.20 per subscriber. The firm expects recommendations regarding he pricing of these new program tiers. Analysis First I downloaded the data from internet which includes number of sports and music subscriber and income for eachmarket 1 and 2. (Table 1) Table 1

Price

Number of Sports Subscribers (Market 1)

Number of Music Subscribers (Market 2)

Income (Market 1)

Number of Sports Subscribers (Market 2)

Number of Music Subscribers (Market 2)

Income (Market 2)

$1.40

4859

6565

$32,472.00

6780

4386

$30,888.00

$1.60

5631

7920

$39,868.00

8401

4950

$37,923.00

$1.80

4499

6554

$48,437.00

7119

3862

$46,075.00

$2.00

2703

4065

$39,414.00

4509

2272

$37,491.00

$2.20

3169

4904

$44,924.00

5545

2614

$42,733.00

$2.40

2100

3335

$31,324.00

3837

1702

$29,797.00

$2.60

1976

3216

$34,397.00

3759

1576

$32,719.00

$2.80

1767

2940

$42,692.00

3488

1389

$40,610.00

$3.00

1390

2361

$52,341.00

2841

1078

$49,788.00

$3.20

1342

2324

$54,992.00

2832

1027

$52,310.00

$3.40

1041

1836

$44,721.00

2265

787

$42,540.00

$3.60

1074

1927

$45,558.00

2404

803

$43,336.00

$3.80

740

1349

$47,367.00

1701

547

$45,057.00

$4.00

860

1593

$50,372.00

2030

630

$47,915.00

$4.20

425

798

$33,988.00

1027

308

$32,331.00

$4.40

350

667

$41,034.00

866

251

$39,033.00

$4.60

316

611

$37,480.00

801

225

$35,652.00

$4.80

359

702

$33,773.00

928

253

$32,126.00

$5.00

313

620

$39,520.00

826

219

$37,593.00

Then I regressed the each subscriber type as an dependent variable along with price and average income for each market as an independent variable. (Table 2, Table 3, Table 4, Table 5) I wrote the regression model for each regression results. Since the P-value of Income is bigger than 0,05 its coefficientis insignificant and therefore I summed up the coefficient of income andconstant of regression model.(beta zero) After I wrote the regression model, I wrote the demand function for each subscribers. Then I manupilated the formula and found P as an inverse demand function. From inverse demand function I found the formula of estimated marginal revenue function. To profit maximize EMR should be equal to MC, therefore I equated the EMR and MC and calculated the profit maximize quantity and profit maximize price for each type of subscribers. Table 2

Number Of Sport Subscriber Market 1

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.91268416

R Square

0.832992377

Adjusted R Square

0.812116424

Standard Error

708.3802456

Observations

19

ANOVA

df

SS

MS

F

Significance F

Regression

2

40045857.47

20022928.74

39.90200497

6.05188E-07

Residual

16

8028841.158

501802.5724

Total

18

48074698.63

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

6767.39283

1115.161914

6.068529371

1.62772E-05

4403.355194

9131.430465

4403.355194

9131.430465

Price

-1320.237102

148.3596664

-8.898895062

1.3568E-07

-1634.745543

-1005.728662

-1634.745543

-1005.728662

Income (Market 1)

-0.016857287

0.023910927

-0.705003507

0.490944558

-0.067546188

0.033831613

-0.067546188

0.033831613

Regression Model:

Quantity = 6767.39 - 1320.23 Price -0.016 Income + e

Quantity = 9182.60 - 1831.75 Price - 0.011 Income + e

Quantity = 9182.60 - 1831.75 Price -(0.011 *39733.7)+ e

Quantity = 9182.60 - 1831.75 Price - 437.07+ e

Linear Demand Function

Q= 8745.53 - 1831.75 P

Inverse Demand Function

P= 4.77 - (1/ 1831.75) Q

Estimated Marginal Revenue:

EMR = 4.77 - 2/ 1831.75 Q

Profit Maximization Quantity

EMR = 4.77 - 2/ 1831.75 Q

Marginal Cost = $ 1.20

Estimated Marginal Revenue = Marginal Cost

4.77 - (2 / 1831.75) Q = 1.20

Q=3570

Profit Maximization Price

P= 4.77 - (1/ 1831.75) Q

P= 4.77 - (1/ 1831.75) 3570

P= 2.99

Table 4

NUMBER OF SPORT SUBSCRIBERS MARKET 2

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.936277591

R Square

0.876615727

Adjusted R Square

0.861192693

Standard Error

857.17285

Observations

19

ANOVA

df

SS

MS

F

Significance F

Regression

2

83523031.28

41761515.64

56.83808517

5.37129E-08

Residual

16

11755924.72

734745.2947

Total

18

95278956

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

9451.513145

1349.395203

7.004258741

2.9736E-06

6590.923123

12312.10317

6590.923123

12312.10317

Price

-1913.860722

179.5220953

-10.66086444

1.11952E-08

-2294.430561

-1533.290884

-2294.430561

-1533.290884

Income (Market 2)

-0.001662905

0.030417078

-0.054670096

0.957078129

-0.066144228

0.062818419

-0.066144228

0.062818419

Regression Model

Quantity = 9451.51 - 1913.86 Price - 0.0016 Income + e

Quantity = 9451.51 - 1913.86 Price - (0.0016* 37795.85)+ e

Quantity = 9451.51 - 1913.86 Price - 60.47+ e

Quantity = 9391.04 - 1913.86 Price - 60.47+ e

Linear Demand Function

Q= 9330.57 - 1913.86 P

Inverse Demand Function

P= 4.87- (1 / 1913.86) Q

Estimated Marginal Revenue:

EMR = 4.87 - (2 / 1913.86) Q

Profit Maximization Quantity

EMR = 4.87 - (2 / 1913.86) Q

Marginal Cost = $ 1.45

Estimated Marginal Revenue = Marginal Cost

4.87 - (2 / 1913.86) Q = 1.45

Q=3420

Profit Maximization Price

P= 4.87 - (1 / 1913.86) Q

P= 4.87 - (1 / 1913.86) 3420

P= 3.16

Table 5

NUMBER OF MUSIC SUBSCRIBERS MARKET 2

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.902072035

R Square

0.813733957

Adjusted R Square

0.790450701

Standard Error

670.0219016

Observations

19

ANOVA

df

SS

MS

F

Significance F

Regression

2

31379551.37

15689775.68

34.9493205

1.449E-06

Residual

16

7182869.577

448929.3486

Total

18

38562420.95

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

6063.359025

1054.774821

5.748486693

2.99214E-05

3827.336306

8299.381744

3827.336306

8299.381744

Price

-1165.883151

140.3261147

-8.308383325

3.38328E-07

-1463.361224

-868.4050792

-1463.361224

-868.4050792

Income (Market 2)

-0.020424367

0.023775961

-0.85903432

0.403008554

-0.070827152

0.029978419

-0.070827152

0.029978419

Regression Model

Quantity= 6063.35 - 1165.88 Price - 0.02 Income + e

Quantity= 6063.35 - 1165.88 Price - (0.02*37795.85) + e

Quantity= 6063.35 - 1165.88 Price - 755.9 + e

Quantity= 5307.45 - 1165.88 Price

Linear Demand Function

Quantity= 5307.45 - 1165.88 Price

Inverse Demand Function

P= 4.55 - (1/1165.88) Q

Estimated Marginal Revenue:

EMR = 4.55 - 2/1165.88 Q

Profit Maximization Quantity

EMR = 4.55 - 2/1165.88 Q

Marginal Cost = $ 1.20

Estimated Marginal Revenue = Marginal Cost

4.55 - (2 / 1165.88) Q = 1.20

Q=1970

Profit Maximization Price

P= 4.55 - (1/1165.88) Q

P= 4.55 - (1/1165.88) 1970

P = 2.88

1)Which of the following is not a kind of price discrimination? A)First-Degree Price Discrimination B) Second-Degree Price Discrimination C) Third-Degree Price Discrimination D) Fourth-Degree Price Discrimination 2)At which point the manager maximize the profit A)MR > MC B)MR=MC C)MR<MC D)Neither 3 -Students have price elasticity of demand for launchof -3 and employees have an elasticity of -1. What should be the pricing policy to maximize profit a)to advertise more efficiently b)to sell the product at high price for both two types ofcustomers c)to sell at lower price for students and sell higher price for employees d)to sell at lower price for employees and sell higher price for students. 4 -In order to understand the significance of independent variable one of the way is A)Looking at adjusted R square, if adjusted R square is high, the coefficient ofvariable is significant B)Looking at R square, if R square is low, the coefficient ofvariable is significant C)Looking at standard error D)Looking at P-Value of each variable. 5- In order to maximize total revenue which one is true A charging the lower price in more elastic market and the higher price in the less elastic market. B charging the lower price in less elastic market and the higher price in the more elastic market. C charging the same price for each market D neither

----

[1] Managerial Economics, Charles Maurice and Christopher R. Thomas, 7. Ed. Mc Graw Hill Irwin,2002 p.613 [2] Managerial Economics, Charles Maurice and Christopher R. Thomas, 7. Ed. Mc Graw Hill Irwin,2002 p.615 [3] Managerial Economics and Business Strategy, Michael R. Baye, Mc Graw Hill, p.407, 2009 [4] Profitable Pricing When market Segments Overlap, Etan Gerstner and Duncan Holthausen, Marketing Science, Vol.5 No.1 Winter 1986. [5] Managerial Economics, Charles Maurice and Christopher R. Thomas, 7. Ed. Mc Graw Hill Irwin,2002 p.615

MEMO 14Third-Degree Price DiscriminationFirms can take advantage of the differences in consumersâ€™ demand in order to increase their profit. Price discrimination is the method by which this is accomplished. Price Discrimination means that the firm charges different prices for the same good. To practice price discrimination successfully, firms need knowledge of the distribution of consumersâ€™ willingness to pay. Certain conditions are necessary for the firm to be able to price-discriminate.

The analysis of price discrimination is a straightforward application of the MR=MC rule.[2] The firm should equate the marginal revenue from selling output to each group to marginal cost.[3]

MR1=MC

MR2=MC

And

MR1 = MR2

The model of thirdâ€“degree monopolistic price discrimination, a monopolist is assumed to sell a homegeneouos product at different prices to market segments that do not overlap. The markets are assumed, therefore, to be perfectly scaled, that is consumers in one market are not allowed to purchase in the other markets.[4]

A manager who wishes to maximize the total revenue in two separate markets should allocate sales between the two markets so that MR1 = MR2 and all units are sold. Although the marginal revenues in the two markets are equal, the prices are charged are not. The higher price will be charged in the market with the less elastic demand and the lower price will be charged in the market having the more elastic demand. In the more elastic market, price could be raised only at the expense of a large decrease in sales. In the less elastic market, higher prices bring less reduction in sales.[5]

MR = P( 1+ 1/E)

MR= Marginal Revenue

P= Price

E= Elasticity

To maximize profit, a firm produces the output at which the marginal revenue to each group equals marginal costs.

MR1= P1(1+1/E1)=MC

MR2= P2 (1+1/E2)=MC

And

MR1= P1(1+1/E1) = MR2= P2 (1+1/E2)

Since MR1 and MR2 must both be positive, E1 and E2 must both be greater (in absolute value) than one.

P1 < P2

and

|E1| >|E2|

A manager who price-discriminates in two separate markets, will maximize total revenue by charging the lower price in more elastic market and the higher price in the less elastic market.

Memo-14 Sports and MusicsFirm offers two small program packages to whom using their basic package. The first is a sports package which includes NBA TV and the soccer Channel. The second is a music package that includes MTV2 and GAC. There are 2 markets; region 1 and region 2. The firm estimated that incremental cost for the sports package are $ 1.45 per subscriber and the incremental cost for the music package are $1.20 per subscriber. The firm expects recommendations regarding he pricing of these new program tiers.

Analysis

First I downloaded the data from internet which includes number of sports and music subscriber and income for each market 1 and 2. (Table 1)

Table 1

Then I regressed the each subscriber type as an dependent variable along with price and average income for each market as an independent variable. (Table 2, Table 3, Table 4, Table 5) I wrote the regression model for each regression results. Since the P-value of Income is bigger than 0,05 its coefficient is insignificant and therefore I summed up the coefficient of income and constant of regression model.(beta zero)

After I wrote the regression model, I wrote the demand function for each subscribers. Then I manupilated the formula and found P as an inverse demand function. From inverse demand function I found the formula of estimated marginal revenue function.

To profit maximize EMR should be equal to MC, therefore I equated the EMR and MC and calculated the profit maximize quantity and profit maximize price for each type of subscribers.

Table 2

Number Of Sport Subscriber Market 1Regression StatisticsdfSSMSFSignificance FCoefficientsStandard Errort StatP-valueLower 95%Upper 95%Lower 95.0%Upper 95.0%Regression Model:Linear Demand FunctionInverse Demand FunctionEstimated Marginal Revenue:Profit Maximization QuantityQ=2126Profit Maximization PriceP= 3.15Table 3

Regression StatisticsdfSSMSFSignificance FCoefficientsStandard Errort StatP-valueLower 95%Upper 95%Lower 95.0%Upper 95.0%Regression Model:Linear Demand FunctionInverse Demand FunctionEstimated Marginal Revenue:Profit Maximization QuantityQ=3570Profit Maximization PriceP= 2.99Table 4

NUMBER OF SPORT SUBSCRIBERS MARKET 2Regression StatisticsdfSSMSFSignificance FCoefficientsStandard Errort StatP-valueLower 95%Upper 95%Lower 95.0%Upper 95.0%Regression ModelLinear Demand FunctionInverse Demand FunctionEstimated Marginal Revenue:Profit Maximization QuantityQ=3420Profit Maximization PriceP= 3.16Table 5

NUMBER OF MUSIC SUBSCRIBERS MARKET 2Regression StatisticsdfSSMSFSignificance FCoefficientsStandard Errort StatP-valueLower 95%Upper 95%Lower 95.0%Upper 95.0%Regression ModelLinear Demand FunctionInverse Demand FunctionEstimated Marginal Revenue:Profit Maximization QuantityQ=1970Profit Maximization PriceP = 2.881) Which of the following is not a kind of price discrimination?

A)First-Degree Price Discrimination

B) Second-Degree Price Discrimination

C) Third-Degree Price Discrimination

D) Fourth-Degree Price Discrimination

2)At which point the manager maximize the profit

A) MR > MC

B) MR=MC

C) MR<MC

D) Neither

3 -Students have price elasticity of demand for launch of -3 and employees have an elasticity of -1. What should be the pricing policy to maximize profit

a) to advertise more efficiently

b) to sell the product at high price for both two types of customers

c) to sell at lower price for students and sell higher price for employees

d) to sell at lower price for employees and sell higher price for students.

4 -In order to understand the significance of independent variable one of the way is

A) Looking at adjusted R square, if adjusted R square is high, the coefficient of variable is significant

B) Looking at R square, if R square is low, the coefficient of variable is significant

C) Looking at standard error

D) Looking at P-Value of each variable.

5- In order to maximize total revenue which one is true

A charging the lower price in more elastic market and the higher price in the less elastic market.

B charging the lower price in less elastic market and the higher price in the more elastic market.

C charging the same price for each market

D neither

----

[1] Managerial Economics, Charles Maurice and Christopher R. Thomas, 7. Ed. Mc Graw Hill Irwin,2002 p.613

[2] Managerial Economics, Charles Maurice and Christopher R. Thomas, 7. Ed. Mc Graw Hill Irwin,2002 p.615

[3] Managerial Economics and Business Strategy, Michael R. Baye, Mc Graw Hill, p.407, 2009

[4] Profitable Pricing When market Segments Overlap, Etan Gerstner and Duncan Holthausen, Marketing Science, Vol.5 No.1 Winter 1986.

[5] Managerial Economics, Charles Maurice and Christopher R. Thomas, 7. Ed. Mc Graw Hill Irwin,2002 p.615