Question

14) The demand equation for a monopolist's product is p = 200 - 0.989, where p is the price per unit (in dollars) of producing q units. If the total cost c (in dollars) of producing 8 units is given by c= 0.02q2 + 2q + 8000, find the level of production at which profit is maximized. 15) The demand function for a monopolist's product is p = 100 – 39, where p is the price per unit (in dollars) for q units. If the average cost c (in dollars) per unit for q units is c = 4 + 100 100, find the output q at which profit is maximized.

Answer 1

14. Monopolist maximizes profit according to the rule Marginal Revenue (MR) = Marginal Cost (MC)
Total Revenue, TR = p*q = (200 - 0.98q)*q = 200q - 0.98q²
MR = d(TR)/dq = 200 - 2*(0.98q) = 200 - 1.96q

MC = dc/dq = 2*(0.02q) + 2 = 0.04q + 2

So, MR = MC gives,
200 - 1.96q = 0.04q + 2
So, 0.04q + 1.96q = 200 - 2
So, 2q = 198
So, q = 198/2 = 99
So, q = 99

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