Because there is only one monopolist in the market under the condition of complete monopoly, the demand curve of the market is the demand curve of the monopolist, and the demand curve can be roughly divided into linear demand function and nonlinear demand function.
1, under the condition of complete monopoly, the linear demand function and its income function or curve can set the demand function as P=n-mq at this time, so there is a total income curve TR=Pq=nq-mq2, and the corresponding average income at this time is AR=TR/q=n-mq, so it can be seen that AR=P=n-mq.
2, when the demand function is a nonlinear function, let P=P(q), then the total income function formula TR=P(q)×q average income function formula AR=TR/q=P, then there is AR=P=P(q), so it can be seen from the above deduction that no matter what form the demand function is, there is always P=AR in the case of complete monopoly.
Extended data:
Precautions:
1. This happens when the price elasticity of demand approaches infinity and the demand curve becomes horizontal, indicating that the smallest change in price will cause great changes in demand.
2. When the elasticity is exactly equal to 1, that is, the demand changes in proportion to the price, the demand curve has unit elasticity.
3. Because the price elasticity of demand measures the degree of response of demand to price, it is related to the slope of demand curve.
4. The demand curve (the change of demand) to the left and to the right respectively indicates the decrease or increase of the quantity of goods that consumers are willing and able to buy due to the change of other factors under the condition of constant price.
Baidu Encyclopedia-Average Income
Baidu Encyclopedia-Completely monopolizing the market
Baidu Encyclopedia-Demand Curve