Consider a monopolist selling two different goods, 91 and 92, whose demands are interdependent. and given...

 

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Consider a monopolist selling two different goods, 91 and 92, whose demands are interdependent. and given by qi=a-bpi+gpj where i and j denotes two products produced by the monopoly, b>0, which guarantees that the demand for a particular good decreases in its own price. The cross-price effect is embodied in parameter g. Assume that lg] <b, such that the own-price effect, represented in parameter b dominates the cross-price effect represented by parameter g. Intuitively, the demand for good i is more sensitive to a given increase in its own price than to the same increase in the price of a different good. Finally, consider that a > c(b-g), hich guarantees that output is strictly positive in equilibrium, where e denotes the constant marginal and average costs. In order to focus on the interdependence between both products'demands, let us assume that the marginal costs of production coincide across both products. That is, total costs are TC(91-92) = cq₁ +cq₂. (a) Interpret the intuition of the demand function given above. Specifically, discuss under what. scenarios goods i and j are substitutes, complements, or independent? Hint: you shall discuss the value of parameter g. (b) Find the profit-maximizing price for good 1, p₁, and for good 2, P2, for this monopolist. Hint: You may write down the profit function and then firm can choose the price to maximize its profit instead of the level of output. The optimal price of the monopoly that maximize its profit should ultimately be a function of parameters a, c, b, g. (c) Based on your calculation in part b), do monopoly price increase or decrease in the parameter that reflects the cross-price effects, g? Interpret the intuition behind your conclusion. Consider a monopolist selling two different goods, 91 and 92, whose demands are interdependent. and given by qi=a-bpi+gpj where i and j denotes two products produced by the monopoly, b>0, which guarantees that the demand for a particular good decreases in its own price. The cross-price effect is embodied in parameter g. Assume that lg] <b, such that the own-price effect, represented in parameter b dominates the cross-price effect represented by parameter g. Intuitively, the demand for good i is more sensitive to a given increase in its own price than to the same increase in the price of a different good. Finally, consider that a > c(b-g), hich guarantees that output is strictly positive in equilibrium, where e denotes the constant marginal and average costs. In order to focus on the interdependence between both products'demands, let us assume that the marginal costs of production coincide across both products. That is, total costs are TC(91-92) = cq₁ +cq₂. (a) Interpret the intuition of the demand function given above. Specifically, discuss under what. scenarios goods i and j are substitutes, complements, or independent? Hint: you shall discuss the value of parameter g. (b) Find the profit-maximizing price for good 1, p₁, and for good 2, P2, for this monopolist. Hint: You may write down the profit function and then firm can choose the price to maximize its profit instead of the level of output. The optimal price of the monopoly that maximize its profit should ultimately be a function of parameters a, c, b, g. (c) Based on your calculation in part b), do monopoly price increase or decrease in the parameter that reflects the cross-price effects, g? Interpret the intuition behind your conclusion.

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Intuition of the Demand Function The demand function given above captures the interdependence betwee... View the full answer