An economist is interested in the variation of the price of a single product. It is obse...

An economist is interested in the variation of the price of a single product. It is observed that a high price for the product in the market attracts more suppliers. However, increasing the quantity of the product supplied tends to drive the price down. Over time, there is an interaction between price and supply. The economist has proposed the following model, where P_n represents the price of the product at year n, and Q_n represents the quantity.

a. Does the model make sense intuitively? What is the significance of the constants 100 and 500? Explain the significance of the signs of the constants −0.1 and 0.2.

b. Test the initial conditions in the following table and predict the long-term behavior.