Deriving a Firm's Supply Function from a Smoothly Increasing Marginal Cost Curve Using Calculus
In cases where a firm's marginal cost function increases smoothly, calculus, specifically differentiation, can be employed to derive its supply function. This analytical approach, which builds upon foundational cost analysis, allows for the subsequent algebraic determination of the market's equilibrium price and quantity.
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Deriving a Firm's Supply Function from a Smoothly Increasing Marginal Cost Curve Using Calculus
Direct Supply Function: Quantity as a Function of Price (Q = S(P))
A firm operates in a market where it must accept the going price of $12 per unit for its product. The firm's marginal cost (MC) of production, which represents the cost to produce one additional unit, changes with the quantity (Q) it produces. The data is as follows:
- At Q=50, MC = $10
- At Q=60, MC = $11
- At Q=70, MC = $12
- At Q=80, MC = $13
To maximize its profit, what quantity should this firm choose to produce?
Impact of Input Cost Changes on a Firm's Supply
A firm that has the power to influence the market price for its product determines its supply schedule by finding the quantity it wishes to sell at various prices along its marginal cost curve.
Analyzing a Firm's Supply Response to a Price Change
Analyzing a Firm's Supply Response to a Price Change
Evaluating the Relationship Between Marginal Cost and Supply
A firm that accepts the market price for its product determines its profit-maximizing output by producing the quantity where the market price equals the cost of producing one more unit (marginal cost). The firm's marginal cost varies with its production level. Given the following specific points on the firm's marginal cost schedule, match each market price to the corresponding quantity the firm will choose to supply.
Marginal Cost Schedule Points:
- The marginal cost of producing the 80th unit is $15.
- The marginal cost of producing the 120th unit is $20.
- The marginal cost of producing the 150th unit is $25.
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Because a profit-maximizing firm that accepts the market price will produce at a quantity where the price equals its marginal cost, the firm's ___________ curve effectively functions as its supply curve.
A profit-maximizing firm, which accepts the market price for its goods, is operating in equilibrium. The market price for its product then permanently increases. Arrange the sequence of logical considerations and actions the firm undertakes to adjust its supply.
Graphical Determination of a Price-Taker's Profit-Maximizing Output
Supply Curve (Firm vs. Market)
Learn After
Evaluating a Business Strategy
A price-taking firm operates with a total cost function given by TC(q) = 10 + 5q + 2q², where q is the quantity of output. Assuming the firm produces a positive amount of output, what is its supply function, q(P)?
Deriving a Firm's Supply Function from its Cost Structure
Supply Strategy for a Competitive Firm
A price-taking firm wants to determine how much output it should produce at any given market price. The firm knows its total cost of production as a function of quantity. Arrange the following steps in the correct logical order to derive the firm's supply function.
A competitive, price-taking firm has a total cost function given by TC(q) = 100 + 20q - q², where q is the quantity of output. A student correctly calculates the marginal cost as MC(q) = 20 - 2q. The student then concludes that the firm's supply function can be derived by setting the market price (P) equal to this marginal cost function. This conclusion is correct.
A competitive, price-taking firm seeks to determine its supply function based on its production costs. Match each total cost function (TC) with the correct corresponding supply function (q(P)), assuming the firm produces a positive quantity of output.
A competitive, price-taking firm has a total cost function given by TC(q) = 50 + 10q + 0.5q², where q is the quantity of output. The firm's profit-maximizing rule is to produce the quantity where the market price equals the firm's marginal cost. If the current market price is $30, the firm will produce ____ units of output.
A price-taking firm in a competitive market has a supply function given by q(P) = (P - 10) / 4, for any price (P) greater than or equal to 10. Which of the following total cost (TC) functions is consistent with this supply function, where q is the quantity of output?
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Supply Strategy for a Competitive Firm