Direct Supply Function: Quantity as a Function of Price (Q = S(P))
The direct supply function, denoted as , expresses the quantity () of a product that a firm will supply at a specific price (). This function is derived by algebraically rearranging the inverse supply function, , to express in terms of . Consequently, the supply function is the mathematical inverse of the marginal cost function, .
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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.
Impact of a Per-Unit Tax on a Firm's Output Decision
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.
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A firm operating in a competitive market has an inverse supply function given by P = 10 + 2Q, where P is the market price and Q is the quantity the firm produces. Which of the following equations correctly represents this firm's direct supply function, which expresses the quantity supplied as a function of price?
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Deriving and Applying a Firm's Supply Function
A firm's decision on how much to produce (Q) is often linked to the market price (P). The relationship can be expressed in two ways: with price as a function of quantity, or with quantity as a function of price. Match each price-based expression (Term) to its equivalent quantity-based expression (Definition).
For a firm with a linear relationship between price (P) and quantity supplied (Q) expressed as P = c + dQ, where 'c' and 'd' are positive constants, a larger value for the coefficient 'd' indicates that the firm's quantity supplied is more responsive to a change in price.
A competitive firm's production decisions are guided by its inverse supply function, P = 20 + 4Q, where P is the price per unit and Q is the quantity of units produced. To express the quantity the firm is willing to supply as a direct function of the price, the equation must be rearranged. The firm's direct supply function is Q = ____.
The Utility of Different Supply Function Formulations
A profit-maximizing firm operating in a competitive market makes its output decisions based on its production costs and the prevailing market price. To determine the quantity it will offer for sale at any given price, one must derive its direct supply function. Arrange the following steps into the correct logical sequence for this derivation.
A firm's willingness to supply a product is described by the direct supply function Q = -20 + 4P, where Q is the quantity supplied and P is the price per unit. Based on this function, what is the minimum price the firm must receive to be willing to supply any units of the product?
A firm's production plan is described by the direct supply function Q = -10 + 5P, where Q is the quantity supplied and P is the price per unit. What is the most accurate interpretation of the coefficient '5' in this function?
Deriving Market Supply by Aggregating Individual Firm Supplies
Inverse Supply Function