Suppose you have a dataset containing information on the monthly sales of a particular product, as well as the prices of the product and the marketing expenditure on the product. You want to estimate a sales function for the product, which relates the quantity of the product sold to its price and marketing expenditure.

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

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

Y = 500 + 2P - 10M + ?

Where Y is the quantity of the product sold, P is the price of the product, M is the marketing expenditure on the product, and ? is the error term.

Calculate the price elasticity of demand and the advertising elasticity of demand when the price is $10 and the marketing expenditure is $50, and interpret the results. Is the product price-sensitive or price-inelastic, and how does advertising affect sales?