Profit Maximization with Cost Function C(Q) = 50 + 4Q + Q^2 and Inverse Demand P = 100 - 2Q
This example presents a firm's profit maximization problem defined by a specific cost structure and market demand. The firm's total cost of production is given by the quadratic function , and it operates under the market constraint of a linear inverse demand function, .
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CORE Econ
Economics
Introduction to Microeconomics Course
The Economy 2.0 Microeconomics @ CORE Econ
Ch.7 The firm and its customers - The Economy 2.0 Microeconomics @ CORE Econ
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Profit Maximization with Cost Function C(Q)=320+2Q+0.2Q^2 and Inverse Demand P=44−0.5Q
Profit Maximization with Cost Function C(Q) = 50 + 4Q + Q^2 and Inverse Demand P = 100 - 2Q
Profit Maximization for a Bicycle Manufacturer
A company's production costs are described by the total cost function C(Q) = 10Q + 50, and the market demand for its product is represented by the inverse demand function P = 70 - Q. To maximize its profit, what quantity (Q*) should the company produce, and what price (P*) should it charge?
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A firm knows its total cost function and the market's inverse demand function. To find the specific price and quantity that will maximize its profit, it must follow a specific sequence of calculations. Arrange the following steps in the correct logical order.
A firm's production costs are described by the function C(Q) = 20 + 10Q + Q², and the market demand for its product is represented by the inverse demand function P = 70 - 2Q. An analyst correctly determines that the profit-maximizing quantity is Q* = 10. However, in their final step, they calculate the profit-maximizing price to be P* = $220. Which statement best describes the error made in calculating the price?
Evaluating a Suboptimal Production Decision
A firm's production process is described by the total cost function C(Q) = 100 + 4Q². The firm faces a linear inverse demand curve of the form P = A - 2Q, where 'A' is a positive constant representing the maximum possible price. If the firm sets its price at the profit-maximizing level of P* = $80, what must be the value of the constant 'A'?
Impact of a Demand Shift on a Firm's Pricing Strategy
A firm operates with a total cost function C(Q) = 5Q² + 10Q + 50 and faces an inverse demand function P = 100 - 5Q. A consultant advises the firm that to maximize profit, they should produce a quantity of 10 units.
For each firm described by a unique pair of cost and inverse demand functions, match it with its correct profit-maximizing output quantity (Q*).
Learn After
A firm operates with a total cost function given by C(Q) = 50 + 4Q + Q^2 and faces an inverse demand curve of P = 100 - 2Q. To maximize its profit, what quantity (Q) should the firm produce and what price (P) should it charge?
Calculating Maximum Profit
Production Strategy Analysis
A firm's total cost is described by the function C(Q) = 50 + 4Q + Q^2 and it faces an inverse demand of P = 100 - 2Q. Arrange the following steps in the correct logical order to determine the firm's profit-maximizing price and quantity.
A firm's total cost is described by the function C(Q) = 50 + 4Q + Q^2 and it faces an inverse demand of P = 100 - 2Q. At the profit-maximizing level of output, the firm's marginal cost will be equal to the price it charges.
A firm's operations are described by a total cost function C(Q) = 50 + 4Q + Q^2 and an inverse demand function P = 100 - 2Q. Match each economic concept with its correct mathematical expression based on these functions.
Profit Maximization Strategy Derivation
A firm's total cost is C(Q) = 50 + 4Q + Q^2 and it faces an inverse demand of P = 100 - 2Q. To find the profit-maximizing quantity, the firm must set its marginal cost equal to its marginal revenue. The marginal revenue function for this firm is MR = ____.
Analysis of a Flawed Profit Strategy
A company's total cost to produce a quantity (Q) of a product is given by the function C(Q) = 50 + 4Q + Q^2. The price (P) it can charge for each unit is determined by the inverse demand function P = 100 - 2Q. If a new regulation imposes a $4 per-unit tax on the company's output, what will be the resulting change to the company's profit-maximizing quantity and price?