Mathematical coordinate curve
Many people introduce economics as a demand curve, with P on the vertical axis and Q on the horizontal axis, but they often have questions, because they ask for a solution like Q=f(P), which is often considered to be conventional. However, this graph is certainly not unreasonable, and it has a useful economic explanation. I'll say a little more here, hoping to explain the ins and outs of the problem clearly. To answer this question, we must first recall the derivation of the origin of demand curve in neoclassical economics. The origin of demand curve is obtained by giving consumer utility function and budget constraints and solving the maximization of consumer utility under constraints. That is to say, in the case of a given income m, consumers decide the quantity of goods 1 and goods 2 they buy according to the prices of goods 1 and goods 2, so as to maximize their utility. In this sense, the most primitive demand function should be written as. The demand curve that is often seen with P as the vertical axis and Q as the horizontal axis is called anti-demand function in economics, which is why the anti-demand function is so popular that it replaces the original demand function. We still need to see the process of maximizing consumer utility. The key equation for finding the extreme value is that in order to maximize the utility of consumers, the absolute value of marginal substitution rate must be equal to the ratio of price, that is, it exists at the optimal consumption level of commodity 1. To simplify the problem, let the price of commodity 2 be 1. Then under the optimal demand level, the price of commodity 1 is a measure of the quantity of commodity 2 that consumers are willing to give up in order to get more commodity 1. If commodity 2 is abstracted as money spent on all other commodities, the marginal substitution rate is the amount of money that consumers are willing to give up in order to get more commodities 1. At this point, the price of commodity 1 is a measure of marginal willingness to pay. Understand this truth, let's look at a downward sloping demand curve. When q is small, we can see a higher price p from q on the horizontal axis. This means that in the case of a relatively small number of goods, consumers are willing to spend a lot of money to get more goods; When Q is larger, it corresponds to a lower price P, and consumers are only willing to spend less money to get more goods. In this sense, the downward sloping demand curve represents the diminishing marginal willingness of consumers to pay. I wonder if it is logical to look at the demand curve with q as the abscissa and p as the ordinate?