Convex Cost Functions and Increasing Marginal Cost
A firm's cost function, C(Q), is described as convex when its second derivative with respect to 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 is upward-sloping.
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A company's total cost to produce a certain good is described by the function C(Q) = 500 + 20Q + 0.5Q², where C is the total cost in dollars and Q is the quantity of units produced. What is the instantaneous rate of change in total cost (i.e., the marginal cost) when the company is producing 10 units?
A firm's marginal cost of production is constant at $15 per unit. Which of the following functions could represent this firm's total cost (C) as a function of quantity (Q), where C is measured in dollars?
Production Decision Analysis
A manufacturing firm observes that for each additional unit it produces, the cost of producing that specific unit is higher than the one before it. If the firm's total production cost is represented by a continuous function of the quantity produced, C(Q), which of the following statements best describes the shape of this total cost function?
For each given total cost function, C(Q), where Q is the quantity of output, match it with its corresponding marginal cost function, MC(Q).
If a company's total cost function is linear (e.g., C(Q) = a + bQ, where 'a' and 'b' are positive constants), its marginal cost will increase as the quantity of output (Q) increases.
The Calculus of Cost
Critiquing the Marginal Cost Definition
In microeconomic theory, if the total cost of production is represented by a continuous and differentiable cubic function, the point where the marginal cost is at its minimum corresponds to a(n) ___________ on the total cost curve.
Interpreting the Second Derivative of Total Cost
The Inverse Market Supply Curve as the Market's Marginal Cost Curve
Convex Cost Functions and Increasing Marginal 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