In: Economics
Consider the demand given by p = 5-0.5Q and instead of marginal cost being constant it is declining and is given by MC = 6-2Q. Find the profit maximizing output, price and the amount of profit.
P = 5-.5Q
Multiplying above by Q to the both side will give revenue R.
R = 5Q- .5Q^2
Differentiation of above equation w.r.t. Q will give marginal revenue MR.
MR = 5-Q
MC = 6-2Q
For profit maximization,
MR = MC
5-Q = 6-2Q
2Q-Q = 6-5 = 1
Q = 1 ( Profit maximizing quantity)
P = 5-.5*1
P = $4.5 (Profit maximizing price)
Net profit = 1*4.5 – (6-2*1)
Net profit = $.5 (Profit)