# The Profit-Maximizing Monopoly

• Matthias Ruth
• Bruce Hannon
Part of the Modeling Dynamic Systems book series (MDS)

## Abstract

In contrast to the previous chapter, let us assume that you are the proud owner of a firm that holds a monopoly on wooden toys. You are now in a position to simultaneously decide about the levels of output and sales price. However, your firm still competes for the input material wood on a competitive market. The price of wood used to produce toys is given and fixed. A second constraint imposed on you is given by the fact that even though you can set the sales price of your output, consumers will respond to a price change by adjusting the quantity of wooden toys they wish to buy. The relationship between the price that you set for your output and the quantity consumers are willing to buy can be specified with a demand curve. Typically, a demand curve is defined as a function that relates the price consumers are willing to pay to the quantity of a good available to them:
$$P = P(Q) with\frac{{\partial P}}{{\partial Q}} < 0$$
(1)
Given such an inverse relationship between price and demand, how many wooden toys should your firm produce and at what price should they be sold to maximize profits?

### Keywords

Lution Verse Monopoly