Economics- How do i calculate price, output and profit when profit is maximised?
TC = 0.5Q^2 + 10Q
Q = 100 − P
(^2 = squared)
How can i calculate the firms output, price and profit when profit is maximised?
Really stuck!
Answer:
The total cost function implies the marginal cost functioon MC=dTC/dQ=Q+10.
The demand function implies the inverse demand function P=100-Q. Since this function is linear, the marginal revenue function has the same vertical intercept but the marginal function is twice as steep. That is, MR=100-2Q.
Setting MR=MC yields.
100-2Q=Q+10 or 3Q=90 or Q=30 units.
The monopolist can sell each of these units for the price P=100-30=$70/unit, so his revenue is P*Q=70(30)=$2,100.
The total cost of producing 30 units is TC=.5(30^2)+10(30)
=$750, so maximum profit is 2,100-750=$1,350.
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