Imagine you open run a coffee shop in a neighborhood that also has a competitor coffee shop. Suppose the demand for your coffee is given by the function: Q = f(Y, P, Pc) = 0.01Y + 5Pc - 2P2 , where Q is the amount of coffee you sell, Y is the neighborhood average income, P is the price you charge and Pc is the price charged by the competitor.
(a) Use total differentiation to find the approximate change in the demand for your coffee with an increase in income of $5,000, if initially, Y = 40, 000, P = 3.00 and Pc = $3.50.
(b) Use total differentiation to find the approximate change in the demand for your coffee with a simultaneous increase in the price of both your coffee and your competitor's coffee by $1, if initially, Y = 40, 000, P = 3.00 and Pc = $4.00.
(c) Use total differentiation to find the approximate change in the demand for your coffee with a 10% increase in income, the price of your own coffee and the price of your competitor's coffee, if initially, Y = 40, 000, P = 3.00 and Pc = $4.00.