1. The price-demand equations x = f(p, q) and y = g(p, q) represent the num- ber of units demanded of products A and B, respectively, at a price p for 1 unit of product A and a price q for 1 unit of product B. Below are examples of weekly price demand equations for A and B: x = f(p, q) = 800 – 0.9p² + 0.8q² y = g(p, q) = 1500 + 0.4p² – 0.3q² Product A Product B - (a) Find a function R (in terms of two independent variables) to denote the total revenue (in pesos) from selling both products. Find R,(10, 2) and interpret the results. (b) In general, when two products, A and B, tend to be consumed or used together, the products are said to be complementary. Mathematically, this means that f,(p, q) < 0 and g„(p, q) < 0 should both be true. Give an example of two products that are complementary. (c) In general, A and B are said to be competitive (substitute) products if fa(p, q) > 0 and gp(p, q) > 0. Explain what these inequalities mean. (d) If neither conditions in (b) nor (c) are met, the products are neither com- plementary nor competitive. Use the tests above to determine whether the products in the given examples are complementary, competitive, or neither.

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