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Mathematics & Economics

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Math Problem

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# Effective Economics Of Industry Under Perfectly Competitive Market (Math Problem Sample)

Instructions:

The task was about finding the Fix cost, variable cost and profit MAXIMIZATION. The sample is all about economics of industry under perfectly COMPETITIVE market

source..Content:

The demand and cost function for a company is estimated as follows:
P =100- 8Q ------------------------------------------------Eq1
CT= 50 +80Q -10Q2 + 0.6Q3 ----------------------------Eq2
* Solution
From the demand function price of goods manufactured must be less 100 which is less than the quantity sold and the cost function;
Fixed cost=50
Variable cost=80Q-10Q2+0.6Q3
We then explore way to find the following variables;
Total revenue (TR) = P*Q = 100Q –8Q2 --------------------------------------------------Eq3
Marginal revenue (MR) = First order derivative of TR with respect to Q = MR = 100 – 16Q --------------------------------Eq4
Marginal cost (MC) = First order derivative of TC with respect to Q=
MC = 80-20Q+1.8Q2 ---------------------------------------------------------------------Eq5
Average revenue (AR) = 100- 8Q= P ---------------------------------------------------Eq6
This helps to minimize price discrimination
Average cost (AC) it’s the TC/Q i.e. AC= [50/Q] +80 -10Q + 0.6Q2 ---------------------Eq7
We can then equate Marginal Revenue to Marginal Cost using the following step
Step 1
MR=MC
Eq5 = Eq7
100-16Q= 80-20Q+1.8Q2
If we equate all variables, we come up with the following linear equation;
(8) 4Q+1.8Q2-20=0
Using Quadratic formula 1.e. Q=-b±b2-4ac2a where a=4, b=1.8 and c=-20
Q=-4±1.82-(4*4*-20)2*4
If we do the calculation, we w...

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