Convexity of the Market Total Cost Function
The assumption that a market's supply curve slopes upward, which indicates that marginal cost increases with quantity, has a direct implication for the market's total cost function, . This condition means that the total cost function, , is necessarily an increasing and convex function. For further details on the properties of convex functions, readers can refer to section 8.4 of 'Mathematics for Economists: An Introductory Textbook' by Malcolm Pemberton and Nicholas Rau.
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CORE Econ
Introduction to Microeconomics Course
Ch.8 Supply and demand: Markets with many buyers and sellers - The Economy 2.0 Microeconomics @ CORE Econ
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Convexity of the Market Total Cost Function
Calculating Total Cost by Integrating Marginal Cost
Deriving Market Supply from Firm Costs
In a competitive market, the inverse supply function is given by P = 20 + 0.5Q, where P is the market price and Q is the total quantity supplied. What is the market's marginal cost of production when 100 units are being produced?
In a market, if the inverse supply curve is a horizontal line, this implies that the marginal cost of producing an additional unit of the good is constant, regardless of the total quantity already being produced.
Deriving the Inverse Supply Curve from the Market's Total Cost Function
The Rationale Behind Supply and Marginal Cost
A market's inverse supply curve shows the price (P) required for producers to supply a given quantity (Q). This price is equal to the market's marginal cost of producing that quantity. Given this relationship, match each inverse supply function below with the correct description of the market's marginal cost behavior.
A market's inverse supply curve is given by the equation P = 40 + 5Q, where P is the price per unit and Q is the total quantity supplied. If the market decides to increase its output from 20 units to 21 units, the market's total cost of production will increase by approximately $____.
An economist wants to derive and verify the shape of a market's inverse supply curve, starting from the market's total cost function, C(Q). Arrange the following steps in the correct logical sequence to accomplish this.
Analyzing an Unconventional Supply Curve
Evaluating a Price-Setting Regulation
Learn After
In a market where producing each additional unit of a good becomes progressively more expensive as total output increases, the total cost of production for the market, C(Q), must have a specific shape. Given this economic principle, which of the following functional forms for the total cost C(Q), where Q is the total quantity produced, is inconsistent with this principle?
A market's total cost to produce a quantity Q is described by the function C(Q) = 100 + 20Q. This cost structure is consistent with the economic principle of an upward-sloping market supply curve.
Relationship Between Supply Curve and Total Cost Function Shape
Market Cost Function Analysis
Match each mathematical description of a market's total cost function, C(Q), with the corresponding economic characteristic of its marginal cost (MC) and market supply curve. (Note: Marginal cost is the rate of change of the total cost function.)
The Economic Rationale for a Convex Total Cost Function
The economic principle that producing additional units of a good becomes progressively more expensive implies that the market's total cost function, C(Q), is convex. For this to be true mathematically, the second derivative of the total cost function with respect to quantity, C''(Q), must be ____.
Consider a market where the total cost of producing a quantity Q is given by the function C(Q) = 500 + 10Q + 0.2Q². This functional form implies that the minimum price a producer would be willing to accept to supply the 50th unit is less than the minimum price they would accept to supply the 51st unit.
Analyzing a Market's Cost Structure
Arrange the following statements into a logical sequence that explains why an upward-sloping market supply curve implies a specific shape for the market's total cost function, C(Q).