equilibrium price and quantity in case of linear demand function and nonlinear supply function

Understanding Market Demand
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Understanding market demand involves analyzing and quantifying the relationship between the price of a product or service and the quantity that consumers are willing and able to purchase at that price. This relationship is typically represented by the demand function, which can be expressed mathematically in different forms depending on the assumptions and characteristics of the market.
One commonly used mathematical equation to represent demand is the linear demand function. It assumes a linear relationship between the quantity demanded (Q) and the price of the product (P). The linear demand function can be written as:
Q = a - bP
Where: Q = Quantity demanded P = Price of the product a = Intercept term, representing the quantity demanded when the price is zero (or the constant term of the demand function) b = Slope of the demand curve, indicating how the quantity demanded changes in response to a change in price
The equation suggests that as the price of the product increases, the quantity demanded decreases, and vice versa. The intercept term (a) captures factors other than price that influence demand, such as consumer preferences, income, or marketing efforts. The slope (b) represents the price sensitivity of demand, indicating the percentage change in quantity demanded resulting from a 1% change in price.
It's important to note that the linear demand function is just one of many possible functional forms to represent market demand. Other common demand functions include quadratic, logarithmic, and exponential forms, which may capture different aspects of consumer behavior and market dynamics. The choice of the specific demand function depends on the characteristics of the market being analyzed and the availability of data.