The average revenue (demand) for product Q is given by AR = 400 – 2Q and the total cost of Q by: STC = 6000 + 12Q + 3Q2 < Note: this is not a typical cubic function a. Find the price function and then the TR function. See Assignment 3 or 4 for an example. Hint: another name for price is average revenue (AR). b. Write the MR and MC functions below. Remember: MR = dTR/dQ and MC = DSTC/dQ. See Assignment 5 for a review of derivatives. c. What positive value of Q will maximize total profit? Remember: Setting MR = MC and solving for Q will give you the Q that maximizes total profit. The value of Q you get should not be zero or negative. d. Use the price function found in (a) to determine the price per unit that will need to be charged at the Q found in (c). This will be the price you should ask per unit for each unit of Q that maximizes total profit. e. How much total profit will result from selling the quantity found in (c) at the price found in (d)? Remember: profit is TR – STC. f. At what level of Q is revenue maximized? Remember: let MR = 0 and solve for Q. MR = 0 signals the objective of maximizing revenue. g. At what level of Q is average profit per unit maximized? Hint: You found the profit function in (e) above. Average profit is the total profit function (e) divided by Q. To find the level of Q that maximizes average profit, find the first derivative of the average profit function, set this derivative equal to zero and solve for Q.
The average revenue (demand) for product Q is given by AR = 400 – 2Q and the total cost of Q by: STC = 6000 + 12Q + 3Q2 < Note: this is not a typical cubic function a. Find the price function and then the TR function. See Assignment 3 or 4 for an example. Hint: another name for price is average revenue (AR). b. Write the MR and MC functions below. Remember: MR = dTR/dQ and MC = DSTC/dQ. See Assignment 5 for a review of derivatives. c. What positive value of Q will maximize total profit? Remember: Setting MR = MC and solving for Q will give you the Q that maximizes total profit. The value of Q you get should not be zero or negative. d. Use the price function found in (a) to determine the price per unit that will need to be charged at the Q found in (c). This will be the price you should ask per unit for each unit of Q that maximizes total profit. e. How much total profit will result from selling the quantity found in (c) at the price found in (d)? Remember: profit is TR – STC. f. At what level of Q is revenue maximized? Remember: let MR = 0 and solve for Q. MR = 0 signals the objective of maximizing revenue. g. At what level of Q is average profit per unit maximized? Hint: You found the profit function in (e) above. Average profit is the total profit function (e) divided by Q. To find the level of Q that maximizes average profit, find the first derivative of the average profit function, set this derivative equal to zero and solve for Q.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Please help with h.
Transcribed Image Text:The average revenue (demand) for product Q is given by AR = 400 – 2Q and the
total cost of Q by:
STC
6000 + 12Q + 3Q?
< Note: this is not a typical cubic function
a. Find the price function and then the TR function. See Assignment 3 or 4
for an example. Hint: another name for price is average revenue (AR).
b. Write the MR and MC functions below. Remember: MR = dTR/dQ and
MC = DSTC/dQ. See Assignment 5 for a review of derivatives.
c. What positive value of Q will maximize total profit? Remember: Setting
MR = MC and solving for Q will give you the Q that maximizes total
profit. The value of Q you get should not be zero or negative.
d. Use the price function found in (a) to determine the price per unit that
will need to be charged at the Q found in (c). This will be the price you
should ask per unit for each unit of Q that maximizes total profit.
e. How much total profit will result from selling the quantity found in (c) at
the price found in (d)? Remember: profit is TR -
– STC.
f. At what level of Q is revenue maximized? Remember: let MR
solve for Q. MR = 0 signals the objective of maximizing revenue.
= 0 and
g. At what level of Q is average profit per unit maximized? Hint: You found
the profit function in (e) above. Average profit is the total profit function
(e) divided by Q. To find the level of Q that maximizes average profit,
find the first derivative of the average profit function, set this derivative
equal to zero and solve for Q.
h. What price per unit should be charged for unit of Q found in (g)? Simply
plug the Q you got in (g) into the same price function you found in (a)
and also used in (d).
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