You were hired by a local business to help customize and price their products. The firm is a monopoly and currently sells two products. Suppose that demand for the products are given by a logistic demand system with mean utilities for the respective products of a1 = 0.1 and a2 = 0.2. 1. What are the revenue - maximizing prices for these two products? Suppose that the firm has done extensive experimentation, and they believe they have a good idea of the underlying characteristics that drive demand for their products. Specifically, the mean utility for each product is driven by two characteristics: a1 = b1*1 +b2*0 and a2 = b1*1 + b2*0.05, where the tastes of consumers for the characteristics are b 10.1 and b2 = 2 and the numbers scaling them are the current value of the characteristics. Suppose that these characteristics are also related to costs, such that mc1 = c1*1 + c2*0 = 0.01 and mc2 = c1*1 + c2*0.05 = 0.06, where c1 = 0.01 and c2 = 0.01. 2. What are the profit - maximizing prices for these two products as currently configured? The firm is considering altering the attributes of its products and wants your help. Specifically, they're willing to slightly adapt one of the characteristics and then optimally re- price both goods. 3. If you could increase characteristic 1 or 2 by 0.1 units, what would you recommend to the firm if the goal is to maximize profits? Please explain your findings and include MATLAB code for the calculations in 1, 2, and 3.
You were hired by a local business to help customize and price their products. The firm is a monopoly and currently sells two products. Suppose that demand for the products are given by a logistic demand system with mean utilities for the respective products of a1 = 0.1 and a2 = 0.2. 1. What are the revenue - maximizing prices for these two products? Suppose that the firm has done extensive experimentation, and they believe they have a good idea of the underlying characteristics that drive demand for their products. Specifically, the mean utility for each product is driven by two characteristics: a1 = b1*1 +b2*0 and a2 = b1*1 + b2*0.05, where the tastes of consumers for the characteristics are b 10.1 and b2 = 2 and the numbers scaling them are the current value of the characteristics. Suppose that these characteristics are also related to costs, such that mc1 = c1*1 + c2*0 = 0.01 and mc2 = c1*1 + c2*0.05 = 0.06, where c1 = 0.01 and c2 = 0.01. 2. What are the profit - maximizing prices for these two products as currently configured? The firm is considering altering the attributes of its products and wants your help. Specifically, they're willing to slightly adapt one of the characteristics and then optimally re- price both goods. 3. If you could increase characteristic 1 or 2 by 0.1 units, what would you recommend to the firm if the goal is to maximize profits? Please explain your findings and include MATLAB code for the calculations in 1, 2, and 3.
Chapter14: Monopoly
Section: Chapter Questions
Problem 14.6P
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Transcribed Image Text:You were hired by a local business to help customize and price their products. The firm is a monopoly and currently sells
two products. Suppose that demand for the products are given by a logistic demand system with mean utilities for the
respective products of a1 = 0.1 and a2 = 0.2. 1. What are the revenue - maximizing prices for these two products?
Suppose that the firm has done extensive experimentation, and they believe they have a good idea of the underlying
characteristics that drive demand for their products. Specifically, the mean utility for each product is driven by two
characteristics: a1 = b1*1 +b2*0 and a2 = b1*1 + b2*0.05, where the tastes of consumers for the characteristics are b
10.1 and b2 = 2 and the numbers scaling them are the current value of the characteristics. Suppose that these
characteristics are also related to costs, such that mc1 = c1*1 + c2*0 = 0.01 and mc2 = c1*1 + c2*0.05 = 0.06, where
c1 = 0.01 and c2 = 0.01. 2. What are the profit - maximizing prices for these two products as currently configured?
The firm is considering altering the attributes of its products and wants your help. Specifically, they're willing to slightly
adapt one of the characteristics and then optimally re- price both goods. 3. If you could increase characteristic 1 or 2 by
0.1 units, what would you recommend to the firm if the goal is to maximize profits? Please explain your findings and
include MATLAB code for the calculations in 1, 2, and 3.
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