4. This exercise lets you construct demand curves for different populations of consumers. Imagine that each consumer chooses whether to buy the product or not and her willingness to pay (wtp) is denoted by v. (a) There are 100 consumers. The consumers are anonymous, but we use numbers for their names. Consumer 1 has wtp v1 = 198, consumer 2 has wtp v2 = 196, and in general consumer i has wtp 200 2i so that V100 = 0. Construct the demand curve, i.e. for each Q, find price (or prices) P such that the number of consumers with wtp at least P is Q. (b) Compare the demand curve you obtained in part a. to the line P(Q) = 200 2Q in the (Q,P) -coordinate system. Compute the marginal revenue curve for this continuous demand curve. (c) For the rest of this exercise, we use continuous demand curves, but you should interpret them with part a. in mind. Consider another demand curve for another population of size 100 given by P(Q) = 150 Q if Q 100. Notice that the willingnesses to pay in this case are more concentrated in this population than in part a. but the average wtp is the same. Compute the marginal revenue curve (again as a function of Q) for this population. (d) For any A with A > 100 and A 100. Compute the marginal revenue curve for this demand. What is the economic meaning of the case when A = 100? 4. This exercise lets you construct demand curves for different populations of consumers. Imagine that each consumer chooses whether to buy the product or not and her willingness to pay (wtp) is denoted by v. (a) There are 100 consumers. The consumers are anonymous, but we use numbers for their names. Consumer 1 has wtp v1 = 198, consumer 2 has wtp v2 = 196, and in general consumer i has wtp 200 2i so that V100 = 0. Construct the demand curve, i.e. for each Q, find price (or prices) P such that the number of consumers with wtp at least P is Q. (b) Compare the demand curve you obtained in part a. to the line P(Q) = 200 2Q in the (Q,P) -coordinate system. Compute the marginal revenue curve for this continuous demand curve. (c) For the rest of this exercise, we use continuous demand curves, but you should interpret them with part a. in mind. Consider another demand curve for another population of size 100 given by P(Q) = 150 Q if Q 100. Notice that the willingnesses to pay in this case are more concentrated in this population than in part a. but the average wtp is the same. Compute the marginal revenue curve (again as a function of Q) for this population. (d) For any A with A > 100 and A 100. Compute the marginal revenue curve for this demand. What is the economic meaning of the case when A = 100