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


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

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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