A monopolist faces the following demand curve:

P=50-0.5Q

where Q is the quantity demanded and P is the price.

The monopolist's total cost function is given by:

TC=50+4Q where TC is the total cost and Q is the quantity produced.

What is the profit maximizing quantity?

Question

A monopolist faces the following demand curve:

P=50-0.5Q

where Q is the quantity demanded and P is the price.

The monopolist's total cost function is given by:

TC=50+4Q where TC is the total cost and Q is the quantity produced.

What is the profit maximizing quantity?

BlackTom AI · Accepted Answer

First, I will restate the problem in my own words to ensure understanding: a monopolist faces the demand P = 50 - 0.5Q and has total cost TC = 50 + 4Q. We need to find the quantity Q that maximizes profit.

Step 1: Compute total revenue (TR) as a function of quantity Q.
TR = P × Q = (50 - 0.5Q)Q = 50Q - 0.5Q^2.

Step 2: Write the profit function, π(Q).
π(Q) = TR - TC = (50Q - 0.5Q^2) - (50 + 4Q) = -0.5Q^2 + 46Q - 50.

Step 3: Use marginal analysis to find the profit-maximizing quantity.
- Marginal revenue (MR) is the derivative of TR with respect to Q: MR = d(TR)/dQ = 50 - Q.
- Marginal cost (MC) is the derivative of TC with respect to Q: MC = d(TC)/dQ = 4.
Set MR = MC for profit maximization: 50 - Q = 4.
Solving gives Q = 46.

Step 4: (Optional consistency check) compute price and profit at Q = 46.
P = 50 - 0.5 × 46 = 50 - 23 = 27.
TR = 27 × 46 = 1242.
TC = 50 + 4 × 46 = 50 + 184 = 234.
π = TR - TC = 1242 - 234 = 1008.

Conclusion (from the calculation): the profit-maximizing quantity is 46.

A monopolist faces the following demand curve: P=50-0.5Q where Q is the quantity demanded and P is the price. The monopolist's total cost function is given by: TC=50+4Q where TC is the total cost and Q is the quantity produced. What is the profit maximizing quantity?数值题

类似问题

Use the model above to answer the following question. The profit maximizing quantity for the monopoly is?

Figure 16-4Refer to Figure 16-4. How much output will the monopolist produce in order to maximize profit?

Figure 16-4Refer to Figure 16-4. How much output will the monopolist produce in order to maximize profit?

Figure 16-4Refer to Figure 16-4. How much output will the monopolist produce in order to maximize profit?

Figure 16-4Refer to Figure 16-4. How much output will the monopolist produce in order to maximize profit?

Figure 16-4Refer to Figure 16-4. How much output will the monopolist produce in order to maximize profit?

Figure 16-5 The following graph depicts the market situation for a monopoly pastry shop called Bearclaws. Refer to Figure 16-5. Based upon the information shown, how many units will Bearclaws produce to maximize profits?

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A monopolist faces the following demand curve: P=50-0.5Q where Q is the quantity demanded and P is the price. The monopolist's total cost function is given by: TC=50+4Q where TC is the total cost and Q is the quantity produced. What is the profit maximizing quantity?数值题

类似问题

Use the model above to answer the following question. The profit maximizing quantity for the monopoly is?

Figure 16-4Refer to Figure 16-4. How much output will the monopolist produce in order to maximize profit?

Figure 16-4Refer to Figure 16-4. How much output will the monopolist produce in order to maximize profit?

Figure 16-4Refer to Figure 16-4. How much output will the monopolist produce in order to maximize profit?

Figure 16-4Refer to Figure 16-4. How much output will the monopolist produce in order to maximize profit?

Figure 16-4Refer to Figure 16-4. How much output will the monopolist produce in order to maximize profit?

Figure 16-5 The following graph depicts the market situation for a monopoly pastry shop called Bearclaws. ​ ​ ​ Refer to Figure 16-5. Based upon the information shown, how many units will Bearclaws produce to maximize profits?

更多留学生实用工具

希望你的学习变得更简单

Figure 16-5 The following graph depicts the market situation for a monopoly pastry shop called Bearclaws. Refer to Figure 16-5. Based upon the information shown, how many units will Bearclaws produce to maximize profits?