3. MUSEUM MONOPOLY MATH Once the museum has incurred the basic operating cost of 60 to open for the day, the average variable cost (and marginal cost) of serving each visitor is only 2. In other words, the museum's total daily operating cost function is DOC[Q] = 60 + 2Q, where Q is the number of visitors. Meanwhile, the inverse demand function for museum admission is P[Q] = 34 - Q. TIP: We used "average daily operating cost" instead of average total cost when discussing museums. a) If this museum were a commercial, profit-maximizing enterprise, then find its profit. TIP: You'll need to find Q* and P*. Even though you could answer this with a well-drawn graph, show that you can "do the math” to find the correct answer. TIP: This may sound familiar. What did you learn about drawing this graph? ☺ b) Suppose the museum manager set the price at 28, which is not the profit-maximizing price. Find its profit. For the remainder of the problem, suppose that the museum is instead a nonprofit entity. c) The museum could set the breakeven price that allows the firm to earn zero profit. Do the math to find this price, PBE TIPS: Breakeven occurs when price equals ADOC. You should find the larger of the two roots using the quadratic formula, Q* = -b±√b²-4ac 2a d) The museum could set the efficient price that eliminates deadweight loss (DWL). Find this efficient price, PEff, as well as the size of the loss (negative economic profit) at that price. TIP: Efficiency occurs when all the seller serves all of the customers who are willing to pay at least the marginal cost of supplying them. e) The museum could charge a zero price (i.e., free admission), but it would need a government subsidy to cover its loss. How large would that loss be?
3. MUSEUM MONOPOLY MATH Once the museum has incurred the basic operating cost of 60 to open for the day, the average variable cost (and marginal cost) of serving each visitor is only 2. In other words, the museum's total daily operating cost function is DOC[Q] = 60 + 2Q, where Q is the number of visitors. Meanwhile, the inverse demand function for museum admission is P[Q] = 34 - Q. TIP: We used "average daily operating cost" instead of average total cost when discussing museums. a) If this museum were a commercial, profit-maximizing enterprise, then find its profit. TIP: You'll need to find Q* and P*. Even though you could answer this with a well-drawn graph, show that you can "do the math” to find the correct answer. TIP: This may sound familiar. What did you learn about drawing this graph? ☺ b) Suppose the museum manager set the price at 28, which is not the profit-maximizing price. Find its profit. For the remainder of the problem, suppose that the museum is instead a nonprofit entity. c) The museum could set the breakeven price that allows the firm to earn zero profit. Do the math to find this price, PBE TIPS: Breakeven occurs when price equals ADOC. You should find the larger of the two roots using the quadratic formula, Q* = -b±√b²-4ac 2a d) The museum could set the efficient price that eliminates deadweight loss (DWL). Find this efficient price, PEff, as well as the size of the loss (negative economic profit) at that price. TIP: Efficiency occurs when all the seller serves all of the customers who are willing to pay at least the marginal cost of supplying them. e) The museum could charge a zero price (i.e., free admission), but it would need a government subsidy to cover its loss. How large would that loss be?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Question
![3. MUSEUM MONOPOLY MATH
Once the museum has incurred the basic operating cost of 60 to open for the day, the average variable cost (and marginal cost) of
serving each visitor is only 2. In other words, the museum's total daily operating cost function is DOC[Q] = 60 + 2Q, where Q
is the number of visitors. Meanwhile, the inverse demand function for museum admission is P[Q] = 34 - Q. TIP: We used
"average daily operating cost" instead of average total cost when discussing museums.
a) If this museum were a commercial, profit-maximizing enterprise, then find its profit. TIP: You'll need to find Q* and P*.
Even though you could answer this with a well-drawn graph, show that you can "do the math” to find the correct answer.
TIP: This may sound familiar. What did you learn about drawing this graph? ☺
b) Suppose the museum manager set the price at 28, which is not the profit-maximizing price. Find its profit.
For the remainder of the problem, suppose that the museum is instead a nonprofit entity.
c) The museum could set the breakeven price that allows the firm to earn zero profit. Do the math to find this price, PBE
TIPS: Breakeven occurs when price equals ADOC. You should find the larger of the two roots using the quadratic formula,
Q*
=
-b±√b²-4ac
2a
d) The museum could set the efficient price that eliminates deadweight loss (DWL). Find this efficient price, PEff, as well as
the size of the loss (negative economic profit) at that price. TIP: Efficiency occurs when all the seller serves all of the
customers who are willing to pay at least the marginal cost of supplying them.
e) The museum could charge a zero price (i.e., free admission), but it would need a government subsidy to cover its loss. How
large would that loss be?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6871a655-6df9-491d-9e6a-d916a0d3d66e%2Fe065b5cb-3bd5-4523-b8a1-0da33de8eb13%2Fb6d2i5k_processed.png&w=3840&q=75)
Transcribed Image Text:3. MUSEUM MONOPOLY MATH
Once the museum has incurred the basic operating cost of 60 to open for the day, the average variable cost (and marginal cost) of
serving each visitor is only 2. In other words, the museum's total daily operating cost function is DOC[Q] = 60 + 2Q, where Q
is the number of visitors. Meanwhile, the inverse demand function for museum admission is P[Q] = 34 - Q. TIP: We used
"average daily operating cost" instead of average total cost when discussing museums.
a) If this museum were a commercial, profit-maximizing enterprise, then find its profit. TIP: You'll need to find Q* and P*.
Even though you could answer this with a well-drawn graph, show that you can "do the math” to find the correct answer.
TIP: This may sound familiar. What did you learn about drawing this graph? ☺
b) Suppose the museum manager set the price at 28, which is not the profit-maximizing price. Find its profit.
For the remainder of the problem, suppose that the museum is instead a nonprofit entity.
c) The museum could set the breakeven price that allows the firm to earn zero profit. Do the math to find this price, PBE
TIPS: Breakeven occurs when price equals ADOC. You should find the larger of the two roots using the quadratic formula,
Q*
=
-b±√b²-4ac
2a
d) The museum could set the efficient price that eliminates deadweight loss (DWL). Find this efficient price, PEff, as well as
the size of the loss (negative economic profit) at that price. TIP: Efficiency occurs when all the seller serves all of the
customers who are willing to pay at least the marginal cost of supplying them.
e) The museum could charge a zero price (i.e., free admission), but it would need a government subsidy to cover its loss. How
large would that loss be?
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