MEMO 14

Third-Degree Price Discrimination

Firms can take advantage of the differences in consumers’ 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 consumers’ 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 third–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 each market 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 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 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 = 6767.39 - 1320.23 Price - (0.016 * 39733.7 )+ e





Quantity = 6767.39 - 1320.23 Price - 635.728 + e






Quantity = 6131.662 - 1320.23 Price + e















Linear Demand Function
















Q= 6131.662 - 1320.23 P
















Inverse Demand Function
















P= 4.64 - (1/1320.23) Q
















Estimated Marginal Revenue:
















EMR = 4.64 - (2/1320.23) Q
















Profit Maximization Quantity
















EMR = 4.64 - (2/1320.23) Q







Marginal Cost = $ 1.45
















Estimated Marginal Revenue = Marginal Cost






4.64 - (2 / 1320.23) Q = 1.45







Q=2126



































Profit Maximization Price
















P= 4.64 - (1/1320.23) Q







P= 4.64 - (1/1320.23) 2126







P= 3.15











Table 3
















SUMMARY OUTPUT
















Regression Statistics







Multiple R
0.927550658







R Square
0.860350224







Adjusted R Square
0.842894002







Standard Error
881.8698666







Observations
19
















ANOVA









df
SS
MS
F
Significance F



Regression
2
76659153.77
38329576.89
49.28616414
1.44651E-07



Residual
16
12443111.39
777694.4616





Total
18
89102265.16
















Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0%
Intercept
9182.604899
1388.276557
6.614391673
5.95068E-06
6239.590088
12125.61971
6239.590088
12125.61971
Price
-1831.745148
184.6944773
-9.917703955
3.08118E-08
-2223.279946
-1440.210349
-2223.279946
-1440.210349
Income (Market 1)
-0.011089312
0.029766959
-0.372537622
0.714381271
-0.074192446
0.052013822
-0.074192446
0.052013822









Regression Model:
















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 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