Multiple Choice
Refer to the table below. The total cost of producing 199 pizzas is \$1,000, and the total cost of producing 200 pizzas is \$1,005. What is the marginal cost of producing the 200th pizza?
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0. Basic Principles of Economics
Marginal Analysis
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Given an inverse linear demand function P = a - bQ, what is the marginal revenue (MR) function?
A
MR = a - bQ
B
MR = bQ - a
C
MR = a - 2bQ
D
MR = a + bQ
Verified step by step guidance1
Start with the given inverse demand function: \(P = a - bQ\), where \(P\) is price, \(Q\) is quantity, \(a\) and \(b\) are constants.
Recall that total revenue (TR) is price times quantity: \(TR = P \times Q\). Substitute the demand function into this to get \(TR = (a - bQ)Q\).
Simplify the total revenue expression: \(TR = aQ - bQ^2\).
Marginal revenue (MR) is the derivative of total revenue with respect to quantity \(Q\). Differentiate \(TR\) with respect to \(Q\) to find \(MR = \frac{dTR}{dQ}\).
Perform the differentiation: \(MR = \frac{d}{dQ}(aQ - bQ^2) = a - 2bQ\). This is the marginal revenue function corresponding to the given demand.
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