Consider the following benefit and cost functions: B(X) = 600X-12X² and C(X) = 20X²
a) What are the MB and the MC?
b) What level of X maximizes the net benefit?
c) What is the net benefit (NB)?
a) Marginal benefit function (MB) = derivating of total benefit function = 600 - 24X.
Marginal cost function (MC) = derivating of total cost function = 40X.
b) Net benefit = Total benefit - Total cost = 600X -12X2 - 20X2 = 600 - 32X2
Now the level of X that maximizes the net benefit equates MB and MC
600 - 24X = 40X
X = 600/64 = 9.375
C) Net benefit (NB) = 600 - 32*(9.375)^2 = -2212.5
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What will be an ideal response?
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