Perfectly discriminatory monopoly

By omersimanovsky December 24, 2024 4 min read

### Perfectly discriminatory monopoly A perfectly discriminatory monopoly is a monopoly that manages to obtain for each unit it sells the full price that the consumer was willing to pay for it, thus effectively robbing the consumer of all **consumer surplus**. – To simplify the explanation, let’s assume that the monopoly produces a product that is sold to only one consumer. – The consumer’s demand function is `P=100-Q`. – According to the demand function, when there is no production at all, the consumer is willing to pay 100 NIS, for the first unit the consumer is willing to pay 99 NIS, for the second unit 98 NIS, and so on, with the consumer being willing to pay 70 NIS for the 30th unit. For a total of 30 units, the consumer is willing to pay the amount represented by the area of the trapezoid highlighted in Figure 31. The formula for calculating the area of the trapezoid is `(large base + small base)*height/2)`. – The large base is the side on the vertical axis (=100)
– The small base is the parallel side, up to the price willing to pay for the 30th unit (=70)
– The height is the side on the horizontal axis (=30) and hence the area of the trapezoid is 2,550. 2,550 NIS is therefore the maximum amount that the consumer is willing to pay for 30 units. Any amount less than 2,550 NIS that he pays for 30 units will leave the consumer with a surplus called **consumer surplus**. If, for example, he is required to pay only 70 NIS per unit, the consumer will pay a total of 2,100 NIS, and will be left with a consumer surplus of 450 NIS. ### Sophistication in sales Instead of charging the consumer a price that is getting smaller for each additional unit, there are 2 more “subtle” ways to rob the consumer of the full consumer surplus. 1. Package pricing
2. Two-rate pricing #### Package pricing Continuing the previous example, let’s assume that the monopoly does not allow the consumer to purchase individual units, but rather packages the product in a package, with the package containing 30 units. The monopoly sets a price of 2,550 NIS for each package, which, as we have already seen, is the maximum amount that the consumer is willing to pay for 30 units. At this price, no **consumer surplus** will remain. #### Two-rate pricing Let’s assume that the monopoly sells its products in a market located in a closed building and can charge an entry fee to this market. The consumer who pays the entry fee can buy individual units in the market at a uniform price per unit. In other words, there are two rates here: 1. The amount of the market entry fee
2. Unit price Continuing the previous example, the unit price set by the monopoly is 70 NIS, the price that corresponds to 30 units on the demand curve `[P=100-Q] `. At this price, the consumer will purchase 30 units and will be left with a **consumer surplus** of 450 NIS. Since the monopoly knows this, it will charge an entrance fee of 450 NIS and in this way will steal all the **consumer surplus**. This method is very popular in clubs and amusement parks. ### Deciding on the quantity of production The perfect monopoly will produce up to the quantity at which MC equals the price of the product. The explanation: The price of the last unit constitutes the monopoly’s marginal revenue. The marginal price decreases, but does not cause all the units preceding the last unit to be discounted, as happens with a regular monopoly that sets a uniform price. #### Example 1 Example data: – **Cost function**: `TC(Q)= Q^2`
– **Demand function**: `P=90-Q` 1. What quantity will the perfect monopoly sell? What is the revenue and profit?
2. What deal will you offer the consumer if he decides to follow package pricing?
3. What deal will he offer the consumer if he decides to operate under two-rate pricing?

#### Solution – **Production quantity**: 30 pcs `[MC=2Q),(P=90-Q)quad=gtquad(2Q=90-Q)] `
– **The price**: 2,250 NIS (calculation based on a trapezoid: `((90+60)*30)/2=2250`)
– **Monopoly profit**: 1,350 NIS `2250-30^2=`
– **Package pricing**: 30 units for 2,250 NIS.
– **Two-Tier Pricing**:
– 30 pieces at a flat price of 60 NIS. Total: 1800 NIS
– + Entrance fee: 450 NIS
– Total: 2,250 NIS ### Producer Surplus, Consumer Surplus, and Social Welfare Producer surplus is the producer’s revenue (2,250) minus the variable cost of production, represented by the area of the triangle below MC. This area is considered. Result: 900 NIS – **Producer Surplus**: 1,350 NIS [=2250-900]
– **Consumer surplus**: 0
– **Social welfare**: 1,350 NIS [=1350+0] ### Distribution of social welfare in a free market If the market were free, the quantity of production would be determined at the point where MC intersects the demand curve. – `Q=30` units `[2Q=90-Q] `
– `P=60` NIS `[P=90-Q] ` **Consumer surplus** (represented by triangle 1): 450 NIS **Producer surplus** (represented by triangle 2): 900 NIS **Total welfare**: 1,350 NIS **Interpretation**: Total social welfare **in a free market** is equal to social welfare in a regime of **perfect monopoly**. The difference between them is in the internal distribution.