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

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...