In a market for a good, a single national producer, OneBrand, makes Specialthing. There is no international market for the good and no competition from abroad. Thus, the producer has a national monopoly in this niche. It faces a demand curve and a cost function given by the equations below. X is quantity produced and sold. It cannot price discriminate, and must charge a uniform price for all customers.
(1) D: P(X) = 1700 – 8X
(2) C(X) = 10000 + (1/2) X2
a) What is its marginal cost (MC) and average total cost (ATC)?
C (X) = 10000 + (1/2) X2
ATC= 10000/X + (X/2)
b) What is the optimum quantity (X) and price (P) combination?
TR= P. Q
P (X) = (1700-8X) X
TR = 1700X-8X2
MR= dTR/ X
Optimum quantity (X) and (P) is where MR=MC
X= 100 Optimum Quantity
OPTIMAL Price (P)
P = P(X) = 1700 – 8X
P= P (X) = 1700-(8 * 100)
c) What profit does it make if it cannot price discriminate?
TR= (1700 * 100) - (8*1002 )
TC= 10000 + (1/2) 1002
Profit = TR – TC
70,000 – 15000
Profit = 55000
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After some time the interest into the product changes, and the firm also realizes some
Customers have different willingness-to-pay than others. Let us call them type 1 and 2.
The two demand functions for each type are, respectively:
(3) D1: P(X) = 975 – 5X,
(4) D2: P(X) = 525 – 2X.
The cost function has also changed, to C(X) = 25X.
d) If it can implement 3rd degree price discrimination, what are the optimum prices in each of the two markets?
TR 1= P * X
= (975-5X) X
=957X – 5X2 MR= dTR/dX
MR 1 = 975-10X
TC = 25X MC= dTR/ dX
Optimum quantity and price in the first market is
MR 1= MC
975-10X = 25
P = 975- 5(95)
P= 475 Price in the first market
TR 2 = P * X
TR 2= (525 – 2X) X
TR 2 = 525X-2X2
MR 2= 525-4X
MR 2 = MC
525- 4X= 25
P= 525- 2 (100)
P=325 Price in the second Market
e) Please, give examples of challenges to the firm’s ability to implement 3rd degree price discrimination.
Price discrimination refers to the practice where the seller sells the same product to different customers at differentiated prices regardless of the cost of the products. It exists in the presence of three conditions. These conditions are that the consumers have different appeals to the goods or services that they demand the availability of market power of a firm, and the ability to limit arbitrage. Third degree type of price discrimination experiences various challenges especially when firms tend to charge their customers different prices depending on their elasticity of demand. Another challenge is the attempt of firms to charge higher prices to consumers with high elasticity of demand while those with low elasticity of demand are charged less.
Q 2 Oligopoly
In another market, three companies are engaged in Cournot competition. The total (inverse) demand curve is given by equation:
(5) D: P(X) = 100 – 5X.
The firms have different marginal costs (MC). MC1 = 20, MC2 = 30, and MC3 = 40.
a) Explain what a reaction curve.
A reaction curve refers to the relationship that occurs between a firm’s profits maximizing output and the expected amount that its competitors would produce.
b) What are the three equations that define quantities X1, X2,and X3?
TR= 100X- 5X2
MR = 100-10X= MC1= 20
MR= 100-10X =MC2 = 30
MR= 100-10X= MC3 = 40
c) How much does each firm produce?
Quantity produced in Firm 1
Quantity produced in Firm 2
Quantity Produced in firm 3
Q 3 Pricing
Let us consider an on-line entertainment company (e.g. one that broadcasts sport events by employing streaming-technologies on the Internet). It has two types of customers. The type depends upon customer income, which is unobservable. The demand curve for each type is
given by equations and.
(6) DH: PH(qH) = 40 – qH,
(7) DL: PL(qL) = 30 – qL.
Marginal cost (MC) is zero. There are as many high (H) types as low (L) types.
a) Explain why it may be reasonable to model this set-up with MC=0.
The main reason as to setting up the model with marginal cost equaling zero is because the high types equal the low types.
b) Explain why 1st degree price discrimination cannot be implemented.
The first degree price discrimination comes as a result of the ability of the firm to discriminate between consumers. At this level, the firm enjoys the ability to charge the maximum amount of money that each consumer is willing and able to pay for every unit of a given commodity or service (Baker, 2003). Implementing the first degree price discrimination in this case would be very difficult due to the fact that the marginal cost is equal to zero.
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The firm wants to make a menu such that each type self-select into the optimum (for the firm) combination of price and quantity. It wants a menu that looks like this:
Option 1: (AH, qH)
Option 2: (AL, qL),
where Ai is the amount to be paid by customer i = H, L. Here, qi is the quantity customer type i is allowed to enjoy after paying the fee Ai.
The firm considers setting qL
1 equal to the maximum quantity the low (L) type has willingness-to-pay for (hint: demand crosses q-axis) and then set AL
1 equal to the full
consumer surplus for L at this amount.
c) Compute (AL
d) What is the net consumer surplus the high (H) type experiences if s/he poses as the low
type and enters the contract and buys (AL
The firm wants to set qH
1 equal to the maximum quantity the high (H) has willingness-to-pay
for (hint: crosses q-axis).
e) What quantity qH
1 is that and what willingness-to-pay does the high type have for this quantity?
f) In order to give the high type an incentive to choose to buy qH
1 instead of posing as low
(L) type and buying qL
1, what is the maximum amount AH
1 can be?
g) Use the set-up derived in class to compute the optimum quantity to offer the low type and
then use this to construct a menu (AH*, qH*) and (AL*, qL*).
In another market, the firm realizes that it actually faces three customer types, with demand
as given in equations.
(8) DSH: PSH(qSH) = A – qSH,
Problem 4 Pricing Schemes
Two-part tariffs are generally used by sellers for the purpose of increasing their profits. They apparently extract all the gains acquired from trade. The 2-part tariff uses a professional technique of setting the marginal charge to be equal to the marginal cost, and on top of that it sets the fixed fee to be equal to the maximum fixed fee the consumer is willing to pay. This turns out to be the value of the trade with regard to the consumer. Trade is made efficient once marginal charges are set to be equal to marginal costs. The gains from trade are maximized due to the fact that consumers tend to maximize the value of goods minus the cost and hence gains from trade are maximized. The maximal gains from trade are then transferred by the fixed fee to the seller. Quantity discounts are part of Two-part tariffs since the sole declining function of quantity at this point turns out to be the average cost of purchase.
In a case where there exist two charges, a two-part tariff and a non-linear a one and both are offered to consumers. Consumers who have low values for large quantities in this case would definitely prefer the linear charge while those whose large quantity have low value would prefer the two-part tariff. A good example of this type of pricing is the one related to cellular telephone. This type of pricing offers a fixed charge that operates until a certain maximum level is achieved, often in a period of one month and then any additional unit is charged at a high price. This pricing scheme encourages the consumers to purchase more minutes than they generally expect to use as a result of the risk it provides them with. This additional minutes that they purchase are used to mitigate the perceived risk.
4.2 Block pricing
Block pricing is generally illustrated by the presence of both the lower and upper volumes of consumption for each charging level. The difference in the objective of a country or a company leads to the existence of huge variations in pricing schemes of the fixed elements. Generally, arising or a declining block of pricing is spread widely.
A good example that falls under block pricing is the water charges. Different blocks thus have different volumetric rates attached to them. In this case therefore, decreasing or increasing block tariffs results from fall or rise of rates due to increased water consumption. Consumers are categorized differently and are thus charged differently since the charges given are not related to the true cost of water. There is a variation of the water charges in response to the capital and social cost of operating water supply. The poor persons are forced to pay the required price from higher block. This comes as a disadvantage to the large families since they need more water in comparison to the small and high-income families.
4.3 Menu Pricing
Menu pricing concerns price determination of food items on the menu list. This pricing involves two steps that include having a food cost goal and maintaining loyalty to the food cost goal. The basis of any kitchen should be the maintenance of sound food costs through the creation of reasonable price points. It is essential that everything is cost out in the when creating a price menu. An analysis of every sale that takes place as well as the current selling price of all items on the menu is very important. These food cost maintained by a restaurant would definitely vary with the type of restaurant.
4.4 Third Degree Price Discrimination
This type of price discrimination is experienced when firms tend to charge their customers different prices depending on their elasticity of demand (Baker, 2003). Higher prices are charged to consumers with high elasticity of demand while those with low elasticity of demand are charged less.
Bundling is he process that involves the amalgamation of related products together for the purpose of selling them as one unit. This mainly occurs when the seller finds out that a combination of the products is likely to get greater appeal to more the consumers than having the products packaged as different offerings. Arrangements on bundling generally involve a cheaper price and thus it is easily acquired as a bundle than separately. It leads to the creation of a low valued large market which sells products cheaper. A good example of this is the selling of computers software accompanied by floppy discs.
It is a marketing arrangement which involves the designation of a sale in such a manner that if a consumer desires to buy an appealing product, they must also purchase an undesired item. Suppliers of specific popular commodities sells them on an agreement with the consumer would also purchase a less popular item as well.
Q 5 Bundling
Consider three types of customers of equal frequency with these reservation prices for good
1, 2, and the bundle B (1 and 2):
Type R1 R2 RB = R1 + R2
Intellectual 140 330 470
Sporty 260 230 490
Jock 300 190 490
The marginal costs are MC1 = 150, MC2 = 200, MCB = 350.
First, the seller considers implementing simple monopoly prices, i.e. one price for good 1 and another price for good 2 (and no bundles).
a) What are the optimum prices for good 1 and 2?
b) What is the profit with such prices?
The firm realizes it may be possible to increase profits using pure bundling.
c) What is the most profitable price of a bundle, if the firm only sells packages that contain good 1 and 2 (and do not sell 1 and 2 individually)?
Then, it realizes it might also offer customers the possibility of buying single goods as well
as the bundle (mixed bundling). First, it contemplates a combination of the simple monopoly prices and the bundle price. But it soon realizes this is not the best it can do.
d) Then, it realizes it might also offer customers the possibility of buying single goods as well as the bundle (mixed bundling). First, it contemplates a combination of the simple monopoly prices and the bundle price. But it soon realizes this is not the best it can do.
c) Show that there is a mixed bundling scheme with prices of good 1, 2, and the bundle that improves upon the profits of pure bundling.
Simple Monopoly Prices
260 for R1and 230 for R2
Under simple monopoly price the seller will sell 2 goods of R1 and 2 goods for R2
Maximum revenue= (260 * 2) + 230 * 2) =980
COST = (150 * 2) + (200 * 2) = 700
Profit = 980- 700 = 280
470, the seller will sell three bundles.
Maximum revenue 470 * 3= 1470
Cost = 350 * 3 = 1050
Profit = 1470- 1050= 420
More profit is gained under pure bundling than under simple monopoly price or mixed bundling. Therefore the seller should stick to pure bundling to maximize profits.
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