g. At what positive level of Q is marginal profit maximized? You found the profit function in (e) above. Marginal profit is the first derivative of the profit function (e). Next, find the derivative of marginal profit, set it equal to zero, and solve for Q. This is the Q that maximizes marginal profit. h. What price per unit should be charged for each 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).
g. At what positive level of Q is marginal profit maximized? You found the profit function in (e) above. Marginal profit is the first derivative of the profit function (e). Next, find the derivative of marginal profit, set it equal to zero, and solve for Q. This is the Q that maximizes marginal profit. h. What price per unit should be charged for each 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).
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
Given equation and questions I need answered are attached.
Below are the answers to previous questions (A-C) on this assignment.
a. TR = 220Q - Q^2
b. MC = 80 - 60 + Q^2
c. Value of Q that maximizes profit = 14
Transcribed Image Text:g. At what positive level of Q is marginal profit maximized? You found the
profit function in (e) above. Marginal profit is the first derivative of the
profit function (e). Next, find the derivative of marginal profit, set it equal
to zero, and solve for Q. This is the Q that maximizes marginal profit.
h. What price per unit should be charged for each 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).
Transcribed Image Text:The demand for product Q is given by Q = 220-P and the total cost of Q by:
STC
-1000+800-3Q²+Q¹
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The answers you provided is what I got for total profit. I believe marginal profit should be different...
Transcribed Image Text:NAME Megan Schuyler (2) Due 12/3/2022 Show work for credit!
The demand for product Q is given by Q = 220-P and the total cost of Q by:
STC =1000 +80Q -3Q² +
+0²
a
Find the price function and then the TR function. See Assignment 3 or 4 for an
example.
Q=220-P
P=220-Q
TR=(PIQ
TR = (220 – 0J0
TR=220Q - Q²
b. Write the MR and MC functions below. Remember: MR = gTB/dQ and MC =
OSTC/dQ. See Assignment 5 for a review of derivatives.
dTR
= 220Q - Q²
(2200) = 220(1)Q¹-¹ = 220
(Q²) = 2(Q²-¹) = 2Q
dQ
dTR
dQ
dTR
dQ
MR = 220 - 20
PROFIT ANALYSIS
dTC
do (1000) = 0
dQ
dTC
(800) = 80
(3Q²) = 3(2)Q²-¹ = 6Q
(²0²) = (3) 0²-¹ = Q²
dQ
dTC
do
dTC
MC = 80 - 6Q+Q²
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.
MR = MC
220 20 80 - 6Q+Q²
Q²6Q +20 + 80-220 = 0
Q²4Q-140 = 0
Q(Q14) +10(Q14) = 0
(Q + 10) (Q14) = 0
Q10 or Q = 14
Value of Q that maximizes profit would equal 14
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.
P = 220 - Q
P
220 14
PROFIT ANALYSIS
P = 206
A price of 206 should be charged for each unit of Q that maximizes
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.
TR = 206(14) = 2884 total revenue
STC = 1000 + 80Q-3Q² +0³
STC = 1000 + 80(14) — 3(14)² + (14)²
1
STC = 1000 + 1120-3(196) +(2744)
STC = 2120588 +914.67
STC = 2446.67
Profit = TR - STC
Profit = 2884 - 2446.67
Maxiumum Profit = 437.33
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.
Total revenue maximizes when MR = 0.
TR = 220Q - Q²
dTR
MR =
dQ
MR 220 2Q
MR = 0
220-2Q=0
220 = 2Q
PROFIT ANALYSIS
220
Q=2
Q = 110
When Q=110 it will maximize the total revenue
g. At what positive level of Q is marginal profit maximized? You found the profit
function in (e) above. Marginal profit is the first derivative of the profit function (e).
Next, find the derivative of marginal profit, set it equal to zero, and solve for Q. This
is the Q that maximizes marginal profit.
h. What price per unit should be charged for each 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).
Profit2.doc 5-20-21
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