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Convex Cost Functions and Increasing Marginal Cost
A firm's cost function, C(Q), is described as convex when its second derivative concerning quantity is positive, expressed as . This mathematical condition implies that the marginal cost (MC), which corresponds to the first derivative of the cost function, rises as output quantity increases. Consequently, the marginal cost curve for a firm with a convex cost function will be upward-sloping.
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CORE Econ
Economics
Introduction to Microeconomics Course
The Economy 2.0 Microeconomics @ CORE Econ
Ch.8 Supply and demand: Markets with many buyers and sellers - The Economy 2.0 Microeconomics @ CORE Econ
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Variable Unit Costs
Influence of Variable Unit Costs on a Firm's Price and Output Decisions
Fixed vs. Variable Costs
Principle of Increasing Total Costs
Marginal Cost
Further Reading on Costs: Stigler's 'The Theory of Price'
Economies of Scope
Activity: Analysis of a Total Cost Function
Modeling Quantity as a Continuous Variable for Cost Analysis Using Calculus
Convex Cost Functions and Increasing Marginal Cost
A manufacturing firm's total cost (C) to produce a quantity (Q) of items is represented by the function C(Q) = 5,000 + 20Q + 0.5Q². Based only on the structure of this function, what can be determined about the firm's costs?
Analyzing a New Business's Costs
Relationship Between Output and Total Costs
Strategic Analysis of Cost Structures
Match each description of a cost behavior with the corresponding mathematical representation in a firm's total cost function, C(Q), where Q is the quantity of output.
Statement: A firm's total cost to produce a quantity (Q) of a good is described by the function C(Q) = 1000 - 5Q + 0.1Q². This function is a plausible representation of a firm's total costs for all possible positive levels of output (Q > 0).
Interpreting a Firm's Cost Function
A company's total production cost is described by the function C(Q) = 15,000 + 75Q, where Q is the number of units produced. The total expenditure required by the company even if it produces zero units (Q=0) is $____.
Production Technology Choice Analysis
Evaluating a Production Decision
Importance of the Cost Function for a Firm's Output and Pricing Decisions
Constant Unit Cost and Constant Returns to Scale
Modeling Assumption of Constant Unit Cost for Apple Cinnamon Cheerios
Average Cost
Learn After
Cubic Cost Function for the Hypothetical Bakery in Figure E8.1
Figure E8.1: Marginal Cost and Isoprofit Curves for a Bakery with Increasing Marginal Cost
A manufacturing firm has the following total cost schedule for producing a specific good:
Quantity (Q) Total Cost (C) 100 units $5,000 101 units $5,050 102 units $5,105 103 units $5,165 Based on this data, what can you infer about the cost to produce each additional unit?
Analysis of a Firm's Cost Function
A firm with an upward-sloping marginal cost curve necessarily has a convex total cost function.
Production Decision at an Artisanal Furniture Company
A firm is analyzing its production costs. Which of the following total cost functions, C(Q), where Q is the quantity of output, indicates that the cost of producing each additional unit is rising as production increases?
A firm's total cost function, C(Q), describes the total cost of producing a quantity (Q) of output. The marginal cost is the cost of producing one additional unit. Match each total cost function below with the correct description of its marginal cost behavior.
The Relationship Between Cost Function Shape and Marginal Cost
If a firm's total cost curve becomes progressively steeper as output increases, it signifies that the firm is experiencing ____ marginal costs.
A company's total cost of production as a function of quantity is convex. This means the cost of producing one additional unit changes as the total quantity produced changes. You are given the marginal costs for producing the 10th, 50th, and 100th units of output, labeled as MC(10), MC(50), and MC(100) respectively. Arrange these marginal costs in ascending order (from lowest to highest).
Evaluating a Manager's Cost Analysis