18.5 Mathematical methods and models in economics

Problem: Let the dynamic function of the supply of the product be equal to the rate of change in the stock of products and given by the equality \( F\left(x_{t}, p_{t}, \frac{d p_{t}}{d t}\right)=\frac{x_{t}}{p_{t}-\sqrt{x_{t} p_{t}}} \frac{d p_{t}}{d t} \), where \( x_{t} \) is the stock of products; \( p_{t} \) is the price of the product \( d s ; \frac{d p_{t}}{d t} \) is the quantity, characterizing the price change. Determine how the price of the product changes depending on its quality.