2. PRIMARY MARKET PRICING OF ORIGINAL ART Suppose you create a one-of-a-kind sculpture and decide that your reservation price is 350 (i.e., you will supply one unit of your art at any prices at or exceeding 350, but refuse to sell your art and supply zero units at prices below 350). Your demand curve is based on three potential customers, whose willingnesses to pay (WTP) are WTPA = 600, WTPB = 500, and WTPc = 400. There is only one period in this game when you can make a sale, and in that period, you don't know which of the customers is going to show up, though they are equally likely to show up, so the probabilities are Pr[1 shows up] = Pr[2 shows up] Pr[3 shows up] = 1/3. Your challenge is to determine your revenue-maximizing price, which you set before the period begins and cannot change. Assume (as we typically do in ECON) that if someone is indifferent between accepting and rejecting an offer, it will take the action that the modeler prefers; here if the price equals a customer's WTP, then that customer will choose to buy. a) = What price should you charge to maximize expected revenue? TIP: Limit your price search to the three WTPs. b) Now suppose that we change the timing of the game so that there are two periods when customers could shop. You set your price before the first period and cannot change it. In period 1, one of the three customers shows up, (again, they are equally likely to show up) and if your price is no greater than their WTP, they will buy and the game ends. If your price is higher than their WTP, then in the second period one of the two remaining customers shows up (with equal probability, like flipping a coin). Again, if the price is acceptable, then they buy, and if not, they do not buy. The game ends with either a sale to a customer or after the two unsuccessful selling periods. What price should you charge to maximize expected revenue? TIP: The six combinations of people who could show up in periods 1 & 2 are customers {1&2, 1&3, 2&1, 2&3, 3&1, 3&2}. Again, check prices 600, 500, and 400. Remember that expected revenue is the average cash inflow, which is different from the total cash inflow. c) Repeat part (b), but now suppose the three WTP's are 900, 500, and 400.
2. PRIMARY MARKET PRICING OF ORIGINAL ART Suppose you create a one-of-a-kind sculpture and decide that your reservation price is 350 (i.e., you will supply one unit of your art at any prices at or exceeding 350, but refuse to sell your art and supply zero units at prices below 350). Your demand curve is based on three potential customers, whose willingnesses to pay (WTP) are WTPA = 600, WTPB = 500, and WTPc = 400. There is only one period in this game when you can make a sale, and in that period, you don't know which of the customers is going to show up, though they are equally likely to show up, so the probabilities are Pr[1 shows up] = Pr[2 shows up] Pr[3 shows up] = 1/3. Your challenge is to determine your revenue-maximizing price, which you set before the period begins and cannot change. Assume (as we typically do in ECON) that if someone is indifferent between accepting and rejecting an offer, it will take the action that the modeler prefers; here if the price equals a customer's WTP, then that customer will choose to buy. a) = What price should you charge to maximize expected revenue? TIP: Limit your price search to the three WTPs. b) Now suppose that we change the timing of the game so that there are two periods when customers could shop. You set your price before the first period and cannot change it. In period 1, one of the three customers shows up, (again, they are equally likely to show up) and if your price is no greater than their WTP, they will buy and the game ends. If your price is higher than their WTP, then in the second period one of the two remaining customers shows up (with equal probability, like flipping a coin). Again, if the price is acceptable, then they buy, and if not, they do not buy. The game ends with either a sale to a customer or after the two unsuccessful selling periods. What price should you charge to maximize expected revenue? TIP: The six combinations of people who could show up in periods 1 & 2 are customers {1&2, 1&3, 2&1, 2&3, 3&1, 3&2}. Again, check prices 600, 500, and 400. Remember that expected revenue is the average cash inflow, which is different from the total cash inflow. c) Repeat part (b), but now suppose the three WTP's are 900, 500, and 400.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![2. PRIMARY MARKET PRICING OF ORIGINAL ART
Suppose you create a one-of-a-kind sculpture and decide that your reservation price is 350 (i.e., you will supply one unit of your
art at any prices at or exceeding 350, but refuse to sell your art and supply zero units at prices below 350). Your demand curve is
based on three potential customers, whose willingnesses to pay (WTP) are WTPA = 600, WTPB = 500, and WTPc = 400. There is
only one period in this game when you can make a sale, and in that period, you don't know which of the customers is going to
show up, though they are equally likely to show up, so the probabilities are Pr[1 shows up] = Pr[2 shows up] Pr[3 shows up] =
1/3. Your challenge is to determine your revenue-maximizing price, which you set before the period begins and cannot change.
Assume (as we typically do in ECON) that if someone is indifferent between accepting and rejecting an offer, it will take the
action that the modeler prefers; here if the price equals a customer's WTP, then that customer will choose to buy.
a)
=
What price should you charge to maximize expected revenue? TIP: Limit your price search to the three WTPs.
b) Now suppose that we change the timing of the game so that there are two periods when customers could shop. You set your
price before the first period and cannot change it. In period 1, one of the three customers shows up, (again, they are equally
likely to show up) and if your price is no greater than their WTP, they will buy and the game ends. If your price is higher
than their WTP, then in the second period one of the two remaining customers shows up (with equal probability, like
flipping a coin). Again, if the price is acceptable, then they buy, and if not, they do not buy. The game ends with either a sale
to a customer or after the two unsuccessful selling periods. What price should you charge to maximize expected revenue?
TIP: The six combinations of people who could show up in periods 1 & 2 are customers {1&2, 1&3, 2&1, 2&3, 3&1, 3&2}.
Again, check prices 600, 500, and 400. Remember that expected revenue is the average cash inflow, which is different from
the total cash inflow.
c) Repeat part (b), but now suppose the three WTP's are 900, 500, and 400.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6871a655-6df9-491d-9e6a-d916a0d3d66e%2F18c79a4c-b61a-4a8d-a6e2-63ddf30b9cfe%2Fh93fyfr_processed.png&w=3840&q=75)
Transcribed Image Text:2. PRIMARY MARKET PRICING OF ORIGINAL ART
Suppose you create a one-of-a-kind sculpture and decide that your reservation price is 350 (i.e., you will supply one unit of your
art at any prices at or exceeding 350, but refuse to sell your art and supply zero units at prices below 350). Your demand curve is
based on three potential customers, whose willingnesses to pay (WTP) are WTPA = 600, WTPB = 500, and WTPc = 400. There is
only one period in this game when you can make a sale, and in that period, you don't know which of the customers is going to
show up, though they are equally likely to show up, so the probabilities are Pr[1 shows up] = Pr[2 shows up] Pr[3 shows up] =
1/3. Your challenge is to determine your revenue-maximizing price, which you set before the period begins and cannot change.
Assume (as we typically do in ECON) that if someone is indifferent between accepting and rejecting an offer, it will take the
action that the modeler prefers; here if the price equals a customer's WTP, then that customer will choose to buy.
a)
=
What price should you charge to maximize expected revenue? TIP: Limit your price search to the three WTPs.
b) Now suppose that we change the timing of the game so that there are two periods when customers could shop. You set your
price before the first period and cannot change it. In period 1, one of the three customers shows up, (again, they are equally
likely to show up) and if your price is no greater than their WTP, they will buy and the game ends. If your price is higher
than their WTP, then in the second period one of the two remaining customers shows up (with equal probability, like
flipping a coin). Again, if the price is acceptable, then they buy, and if not, they do not buy. The game ends with either a sale
to a customer or after the two unsuccessful selling periods. What price should you charge to maximize expected revenue?
TIP: The six combinations of people who could show up in periods 1 & 2 are customers {1&2, 1&3, 2&1, 2&3, 3&1, 3&2}.
Again, check prices 600, 500, and 400. Remember that expected revenue is the average cash inflow, which is different from
the total cash inflow.
c) Repeat part (b), but now suppose the three WTP's are 900, 500, and 400.
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