Two competing brands of power lawnmowers are sold in the same town. The price of the first brand is x dollars per mower, and the price of the second brand is y dollars per mower. The local demand for the first brand of mower is given by a function D(x, y).

a. How would you expect the demand for the first brand of mower to be affected by an increase in x? By an increase in y?

b. Translate your answers in part (a) into conditions on the signs of the partial derivatives of D.

c. If D(x, y) = a + bx + cy, what can you say about the signs of the coefficients b and c if your conclusions in parts (a) and (b) are to hold?