Assume the demand schedule below and TC function below to find maximize profit, Total Revenue (TR), Total Cost(TC), and max profit. Using the MR=MR (Marginal Revenue) approach or Excel (Solver).
P = 10 - .5Q
TC = 10 + Q - .4Q2
Demand function is given as
P = 10 - 0.5Q
So total Revenue = TR = P*Q = 10Q - 0.5 * Q^2
Marginal Revenue = MR = d/dQ TR = d/dQ (10Q - 0.5*Q^2) = 10 - Q
Total COst = TC = 10 + Q - 0.4*Q^2
Marginal Cost = MC = d/dQ TC = d/dQ (10 + Q - 0.4*Q^2) = 1 - 0.8Q
At profit maximization, MR = MC
or 10 - Q = 1 - 0.8Q
or 0.2Q = 9
or Q = 45
P = 10 - 0.5*Q = 10 - 0.5*45 = 10 - 22.5 = -12.5
Total Revenue = 10Q - 0.5 * Q^2 = 10*45 - 0.*45^2 = -562.50
Total Cost = 10 + Q - 0.4*Q^2 = 10 + 45 - 0.4*45^2 = -755
Total Profit = Total Revenue - Total Cost = -562.50 - (-755) = 192.50
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