Pre-mixed concrete is an important input for the construction industry. Concrete cannot be stored or transported over long distances as it begins to set after only a few hours. For this reason, only the three local firms—Aggregate Inc., Big Industries and ConCorp—are in a position to compete in the market. Moreover, the capital and regulatory requirements for constructing a new concrete plant are substantial, creating an effective barrier to entry. Pre-mixed concrete is regarded as a homogeneous good by the construction industry. Inverse demand in the market has been estimated to be, P = 670 − Q/40, where P represents the price of a cubic metre of concrete in dollars, and Q is the total number of cubic metres of concrete supplied into the market on a given day. At present the three firms appear have identical production costs, with each firm facing fixed costs of $400,000 per day and a marginal cost of $190 per cubic metre. Big Industries and ConCorp estimate that the proposed merger would reduce their marginal cost to $145 per cubic metre, while the merged firm is expected to face fixed costs of $600,000 per day. Now suppose that the merger takes place and that the merged firm achieves the expected efficiencies. (Note that Aggregate Inc.’s costs are not be affected by the merger.) Step 5: Find the new equilibrium quantities and price for the market. Use QA to denote the quantity produced by Aggregate Inc., and QB to denote the quantity produced by the merged firm, BigCon.  Step 6: Find the new equilibrium firm profits and consumer surplus. Also reocommend if the merger is permitted to proceed or not.

ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
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hi im done with steps 1-4 but i really need help for steps 5-6. I'll attach my answers image form thanks. 

Pre-mixed concrete is an important input for the construction industry. Concrete cannot be stored or transported over long distances as it begins to set after only a few hours. For this reason, only the three local firms—Aggregate Inc., Big Industries and ConCorp—are in a position to compete in the market. Moreover, the capital and regulatory requirements for constructing a new concrete plant are substantial, creating an effective barrier to entry. Pre-mixed concrete is regarded as a homogeneous good by the construction industry. Inverse demand in the market has been estimated to be,
P = 670 − Q/40,
where P represents the price of a cubic metre of concrete in dollars, and Q is the total number of cubic metres of concrete supplied into the market on a given day. At present the three firms appear have identical production costs, with each firm facing fixed costs of $400,000 per day and a marginal cost of $190 per cubic metre. Big Industries and ConCorp estimate that the proposed merger would reduce their marginal cost to $145 per cubic metre, while the merged firm is expected to face fixed costs of $600,000 per day.

Now suppose that the merger takes place and that the merged firm achieves the
expected efficiencies. (Note that Aggregate Inc.’s costs are not be affected by the merger.)
Step 5: Find the new equilibrium quantities and price for the market. Use QA to denote the quantity produced by Aggregate Inc., and QB to denote the quantity produced by the merged firm, BigCon. 
Step 6: Find the new equilibrium firm profits and consumer surplus. Also reocommend if the merger is permitted to proceed or not.

Step 1: Profit Function for a Typical Firm
P = 670
Q
40
Q = QA + X
P = 670-
LA
X
40 40
Total Revenue (TR) (QA) = Price *QA =
[670 QA
P = 670
MR(QA) 670
(Q₁+x)
40
670
TR(X) = PX = 670X
MR(X) = 670
MR(QA) = MC
QA
X
20 40
670 - 190
Q²A
40
670-
670 -
Step 2: Best-Response Function for the Typical
Firm
MR(X) = MC
QA
-
190
QAX
40
40 (480-24)
X = 19,200 2QA
QA
X
20 40
QA
20
X
QA
40 20
QA X
40 20
= 190
-
= X
X
40
= 190
X
QA
20 40
X
40
0 (480 - 20) = Q₁
QA
= 19,200 2X
XQA
40
x²
40
Step 3: Equilibrium Quantity for the Typical
Firm, Market Quantity, and Market Price
QA 19,200
=
2X
QA = 19,200
QA = 19,200
3QA = 19,200
QA = 6,400
Which means each firm will sell 6,400
units and the market quantity is 19,200 units.
Q
40
P = 670
P = 670
2(19,200 - 2QA)
38,400 +4QA
P = 670
P = 190
Therefore, the firms will sell the goods for $190
19,200
40
480
=
Step 4: Equilibrium Profit for the Typical Firm
and Consumer Surplus
Profit TR-TC
=
Profit= 19,200(190) – (400,000
+ 19,200 (190))
= 3,648,000 — 4,048,000
= -400,000
Thus, there is a loss of $400,000.
Consumer Surplus
1
2
= 4,608,000
(480)19,200
=
1
(670 – 190)19,200
Transcribed Image Text:Step 1: Profit Function for a Typical Firm P = 670 Q 40 Q = QA + X P = 670- LA X 40 40 Total Revenue (TR) (QA) = Price *QA = [670 QA P = 670 MR(QA) 670 (Q₁+x) 40 670 TR(X) = PX = 670X MR(X) = 670 MR(QA) = MC QA X 20 40 670 - 190 Q²A 40 670- 670 - Step 2: Best-Response Function for the Typical Firm MR(X) = MC QA - 190 QAX 40 40 (480-24) X = 19,200 2QA QA X 20 40 QA 20 X QA 40 20 QA X 40 20 = 190 - = X X 40 = 190 X QA 20 40 X 40 0 (480 - 20) = Q₁ QA = 19,200 2X XQA 40 x² 40 Step 3: Equilibrium Quantity for the Typical Firm, Market Quantity, and Market Price QA 19,200 = 2X QA = 19,200 QA = 19,200 3QA = 19,200 QA = 6,400 Which means each firm will sell 6,400 units and the market quantity is 19,200 units. Q 40 P = 670 P = 670 2(19,200 - 2QA) 38,400 +4QA P = 670 P = 190 Therefore, the firms will sell the goods for $190 19,200 40 480 = Step 4: Equilibrium Profit for the Typical Firm and Consumer Surplus Profit TR-TC = Profit= 19,200(190) – (400,000 + 19,200 (190)) = 3,648,000 — 4,048,000 = -400,000 Thus, there is a loss of $400,000. Consumer Surplus 1 2 = 4,608,000 (480)19,200 = 1 (670 – 190)19,200
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