1. GRANTS & DONATIONS A non-profit modern dance company strives to maximize attendance subject to breaking even. It produces shows according to the cost function, C[Q] = 60 + 7Q, where Q is the quantity of available seats. The inverse demand function is P = 30-Q, where P is the price. a) b) c) d) e) Draw a well-labeled graph showing these curves: demand, marginal revenue, marginal cost, and average total cost. Find the breakeven price. Show how to do the math. TIP: Check your work with your graph! Suppose the company wants to charge a uniform price of eight (P = 8) for each customer. Find the government grant G that would allow the company to break even. Now suppose there is a $40 government grant, and the company determines that if it sets the price at $5 or less, then each of its customers will make a donation of $4. If this company strives to maximize attendance subject to at least breaking even, what price should it set? Assume tickets are indivisible, so consider only integer levels of Q. Finally, suppose instead that the company is able to use first-degree (or perfect) price discrimination, which means that each consumer pays exactly their willingness to pay. To simplify the math, suppose that Q is perfectly divisible. To three decimal places, what quantity Q1DPD will maximize attendance subject to breaking even? HINT: There are no grants or donations.
1. GRANTS & DONATIONS A non-profit modern dance company strives to maximize attendance subject to breaking even. It produces shows according to the cost function, C[Q] = 60 + 7Q, where Q is the quantity of available seats. The inverse demand function is P = 30-Q, where P is the price. a) b) c) d) e) Draw a well-labeled graph showing these curves: demand, marginal revenue, marginal cost, and average total cost. Find the breakeven price. Show how to do the math. TIP: Check your work with your graph! Suppose the company wants to charge a uniform price of eight (P = 8) for each customer. Find the government grant G that would allow the company to break even. Now suppose there is a $40 government grant, and the company determines that if it sets the price at $5 or less, then each of its customers will make a donation of $4. If this company strives to maximize attendance subject to at least breaking even, what price should it set? Assume tickets are indivisible, so consider only integer levels of Q. Finally, suppose instead that the company is able to use first-degree (or perfect) price discrimination, which means that each consumer pays exactly their willingness to pay. To simplify the math, suppose that Q is perfectly divisible. To three decimal places, what quantity Q1DPD will maximize attendance subject to breaking even? HINT: There are no grants or donations.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
![1. GRANTS & DONATIONS
A non-profit modern dance company strives to maximize attendance subject to breaking even. It produces shows
according to the cost function, C[Q] = 60 + 7Q, where Q is the quantity of available seats. The inverse demand function
is P = 30-Q, where P is the price.
a)
b)
c)
d)
e)
Draw a well-labeled graph showing these curves: demand, marginal revenue, marginal cost, and average total cost.
Find the breakeven price. Show how to do the math. TIP: Check your work with your graph!
Suppose the company wants to charge a uniform price of eight (P = 8) for each customer. Find the government
grant G that would allow the company to break even.
Now suppose there is a $40 government grant, and the company determines that if it sets the price at $5 or less,
then each of its customers will make a donation of $4. If this company strives to maximize attendance subject to
at least breaking even, what price should it set? Assume tickets are indivisible, so consider only integer levels of
Q.
Finally, suppose instead that the company is able to use first-degree (or perfect) price discrimination, which means
that each consumer pays exactly their willingness to pay. To simplify the math, suppose that Q is perfectly divisible.
To three decimal places, what quantity Q1DPD will maximize attendance subject to breaking even? HINT: There
are no grants or donations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6871a655-6df9-491d-9e6a-d916a0d3d66e%2F2e65f2d9-eaff-405e-9973-f76a7ebd8ca8%2Fkdix5d_processed.png&w=3840&q=75)
Transcribed Image Text:1. GRANTS & DONATIONS
A non-profit modern dance company strives to maximize attendance subject to breaking even. It produces shows
according to the cost function, C[Q] = 60 + 7Q, where Q is the quantity of available seats. The inverse demand function
is P = 30-Q, where P is the price.
a)
b)
c)
d)
e)
Draw a well-labeled graph showing these curves: demand, marginal revenue, marginal cost, and average total cost.
Find the breakeven price. Show how to do the math. TIP: Check your work with your graph!
Suppose the company wants to charge a uniform price of eight (P = 8) for each customer. Find the government
grant G that would allow the company to break even.
Now suppose there is a $40 government grant, and the company determines that if it sets the price at $5 or less,
then each of its customers will make a donation of $4. If this company strives to maximize attendance subject to
at least breaking even, what price should it set? Assume tickets are indivisible, so consider only integer levels of
Q.
Finally, suppose instead that the company is able to use first-degree (or perfect) price discrimination, which means
that each consumer pays exactly their willingness to pay. To simplify the math, suppose that Q is perfectly divisible.
To three decimal places, what quantity Q1DPD will maximize attendance subject to breaking even? HINT: There
are no grants or donations.
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