You work in an economic consultancy and you are asked to analyse a duopoly with product differentiation. The demand for both goods are given by the system: 91a-bp + dp 92 a bp2+dp, where a, b > 0 and [d] < b. d > 0 indicates the products are substitutes, d < 0 indicate complements. The costs of the firms is given by C(q) = ciqi, i = 1,2. Profits are given by: (PP) (a bp,+ dp)(pic), i = 1,2. = - You are asked to perform the following tasks: 1. Build in Python a demand function that has prices, and demand parameters (a, b, d) as inputs. The function should return the quantity demanded for a given firm. 2. Build in Python a cost function that returns the cost that a given firm would incur to produce a certain quantity of output (the inputs should be quantity and the cost paramter).. 3. Build in Python a profit function that returns the profit of a given firm. The user of the function should be able to choose the cost parameter, the price of the firm, the price of the competitor, and the demand parameters. 4. Build in Python a best response function that returns the optimal price of a firm, given cost, the demand parameters, and the competitor's price.