ACP Economics Price Theory Industry Analysis & Production Theory Discussion

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Economics

Anthem College Phoenix

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Explanation & Answer

Attached.

ECONOMICS

Price Theory
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Date

1

ECONOMICS
Industry analysis
Step 1
From production theory, we know that;
𝑇𝐢 = 𝐹𝐢 + 𝑉𝐢
Where;
TC is total cost
FC is the fixed cost
VV is the Variable cost
From the information in the analysis, Fixed Cost = $100, and Marginal cost is 6, thus we can
derive TC from MC giving the following function;
𝑇𝐢 = 100 + 6𝑄𝐴
Step 2
From the analysis;
𝑃 = 42 βˆ’ 0.1𝑄 ,
But, Total Revenue is given as;
𝑇𝑅 = 𝑃 βˆ— 𝑄
Where;
P is the price

2

ECONOMICS
Q is the Quantity produced.
= (42 – 0.1(𝑄𝐴 + 𝑋)
𝑇𝑅 = 42𝑄𝐴 – 0.1𝑄𝐴2 βˆ’ 0.1𝑄𝐴𝑋
π‘ƒπ‘Ÿπ‘œπ‘“π‘–π‘‘ (πœ‹π‘„π΄) = 𝑇𝑅 βˆ’ 𝑇𝐢
πœ‹ (𝑄𝐴) = 42𝑄𝐴 – 0.1𝑄𝐴2 βˆ’ 0.1𝑄𝐴𝑋 βˆ’ 6𝑄𝐴 βˆ’ 100
Collecting the like-terms, we get;
πœ‹ (𝑄𝐴) = 36𝑄𝐴 βˆ’ 0.1𝑄𝐴2 βˆ’ 0.1𝑄𝐴𝑋 βˆ’ 100
Step Three
πœ‹ (𝑄𝐴) = 36𝑄𝐴 βˆ’ 0.1𝑄𝐴2 βˆ’ 0.1𝑄𝐴𝑋 βˆ’ 100
Taking the First order condition with respect to QA;
πœ•πœ‹
= 36 βˆ’ 0.2𝑄𝐴 βˆ’ 0.1𝑋 = 0
πœ•π‘„π΄
36 βˆ’ 0.1𝑋 = 0.2𝑄𝐴
𝑄𝐴 = 180 βˆ’ 0.5𝑋 (Typical firm best response function)
Step Four
From the step three, we can then say that;
Replacing X = (𝑁 βˆ’ 1)𝑄𝐴
π‘„π΄βˆ— =180 βˆ’ 0.5(𝑁 βˆ’ 1)𝑄𝐴
Making QA the subject, we get;

3

ECONOMICS

π‘„π΄βˆ— =

360
𝑁+1

Step Five
Number of firms is equal to N, thus;
π‘„π΄βˆ— =

360
𝑁+1

If we multiply number of firms with the quantity per firm, we get;
π‘„π΄βˆ— = π‘π‘„π΄βˆ— =

360𝑁
𝑁+1

From the analysis, we were given that;
π‘ƒβˆ— = 42 βˆ’ 0.1π‘„π΄βˆ—
We then replace where there is QA in the demand function above as follows;
360𝑁
)
π‘ƒβˆ— = 42 βˆ’ 0.1 (
𝑁+1
π‘ƒβˆ— = 42 βˆ’

36𝑁
𝑁+1

Step Six
Since demand func...


Anonymous
Excellent resource! Really helped me get the gist of things.

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