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Marginal Revenue, Average Costs, and Graph Components

when the inverse demand curve is linear, there’s a simple way to find the profit maximizing level of output

linear inverse demand curve:

P = a-b x Q

marginal revenue curve schedule:

MR = a-2b x Q

profit maximization happens when MR = MC or a-2b = MC

average cost formula:

AC (Q) = TC(Q)/Q

profit margin:

(P-AC(Q))

thinking on the margin = profits are maximized when the monopolist sets MR = MC

given the demand curve, find marginal revenue curve

given total cost curve, find the marginal cost curve

equate marginal revenue to marginal cost

determines quantity produced

given quantity produced, find corresponding price associated with the quantity produced (demand curve)

determine revenues

determine costs

calculate profits

MR = 20-4Q

MC = 8

MR = MC

Q = 3

P = 20-2(3) = 14

PQ = 14(3) = 42

TC (Q) = 8(3) = 24

profits = 18

when the inverse demand curve is linear, there’s a simple way to find the profit maximizing level of output

linear inverse demand curve:

P = a-b x Q

marginal revenue curve schedule:

MR = a-2b x Q

profit maximization happens when MR = MC or a-2b = MC

average cost formula:

AC (Q) = TC(Q)/Q

profit margin:

(P-AC(Q))

thinking on the margin = profits are maximized when the monopolist sets MR = MC

given the demand curve, find marginal revenue curve

given total cost curve, find the marginal cost curve

equate marginal revenue to marginal cost

determines quantity produced

given quantity produced, find corresponding price associated with the quantity produced (demand curve)

determine revenues

determine costs

calculate profits

MR = 20-4Q

MC = 8

MR = MC

Q = 3

P = 20-2(3) = 14

PQ = 14(3) = 42

TC (Q) = 8(3) = 24

profits = 18

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Note

Studied by 35 people

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Note

Studied by 36 people

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Princeton Review AP Calculus BC, Chapter 4: Differentiation: Definition and Basic Derivative Rules

Note

Studied by 81 people

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