This document analyzes the behavior of a monopoly in two different markets, calculating total demand and determining the price that maximizes profit.
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[...] In reality, it chooses the price that maximizes its profit, that is, the difference between sales revenue (price * quantities) and production costs * quantities). The following table is given: Price Total Demand Sales Revenue Production Cost Monopoly Profit 1 12 12 24 -12 2 12 24 24 3 10 30 20 10 4 8 32 16 16 5 7 35 14 21 6 4 24 8 16 7 2 14 4 10 8 We then observe that the profit is maximal for p = 5. With this price of the quantities exchanged are 7 and the monopoly profit is 21. [...]
[...] Profit Maximisation Market 1 To calculate the total demand, we need to calculate the demand of each consumer using the table provided in the statement. This table indicates that consumer A is willing to pay for the first unit of the good, for the second unit, and for the third unit. Thus, if the price set by the monopoly is consumer A will not want to acquire this good. If the price is he will want to buy one unit of the good. [...]
[...] By systematizing this reasoning for all consumers and all possible prices, we obtain the following total demand: Price Demand of cons A Demand of cons B Demand of cons C Demand of cons D Total demand 1 3 3 3 3 12 2 3 3 3 3 12 3 3 2 2 3 10 4 2 2 2 2 8 5 2 1 2 2 7 6 1 1 1 1 4 7 1 1 2 8 One can note in passing that the total demand is a decreasing function of the price, which is logical. Let's now examine the behavior of the monopoly. [...]
[...] We calculate the total demand on this market from the table provided in the statement: Price Demand A Demand B Demand C Demand D Total demand 1 3 3 3 3 12 2 3 3 3 2 11 3 3 3 3 2 11 4 3 3 2 2 10 5 3 2 2 2 9 6 3 2 2 2 9 7 2 2 2 2 8 8 2 2 1 2 7 9 2 1 1 2 6 10 2 1 1 2 6 11 1 1 1 2 5 12 1 1 1 1 4 13 1 1 1 1 4 14 1 1 1 3 15 1 1 2 16 1 1 2 17 1 1 18 1 1 19 And we draw the following table to deduce the behavior of the monopoly: [...]
