Consider the demand given by p = 5-0.5Q and instead of marginal cost being constant it...

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.

Solutions

Expert Solution

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)

Rahul Sunny answered 1 year ago

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