Suppose you are given a dataset containing information on the sales (in units) of a certain product, as well as the price of the product and the income level of the consumers. You want to estimate a demand function for the product, which relates the quantity demanded of the product to its price and the income of the consumers.

a) Write the equation of the demand function and explain the meaning of each of its coefficients.

b) Suppose you estimate the demand function using multiple linear regression with price and income as independent variables. The estimated regression equation is:

Y = 100 - 0.5P + 5I + ?

Where Y is the quantity demanded of the product, P is the price of the product, I is the income of the consumers, and ? is the error term.

Calculate the price elasticity of demand at a price of $10, and interpret the result. Is the product price-sensitive or price-inelastic at this price?