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Exam 2: Optimal Decisions Using Marginal Analysis

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Question 21

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KopyKat is a firm that specializes in printing business cards and résumé's,using the latest laser technology.The manager has estimated that weekly demand can be approximated by P = 25 - 0.001Q,where P is price and Q is output per week.The firm's cost function is C = 25,000 + 13Q + 0.002Q2,where C is total cost. (a)Determine the firm's profit maximizing price and output.

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The payment of $10,000 per month represe...

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Question 22

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The demand for a firm's product is given by the equation: P = 36 - 0.2Q.The firm's cost equation is given by C = 200 + 20Q. (a)Determine the firm's optimal quantity and price.

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With the new cost function,MC = $24.Sett...

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Question 23

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A firm's demand curve is given by Q = 800 - 2P,where P = price and Q = quantity.Therefore,its inverse demand equation is _____.

Suppose a firm's profit is given by the equation $\pi$ = -200 + 80Q - 0.2Q2,where $\pi$ = profit and Q = quantity.Which of the following is true?

For a downward-sloping demand curve,the associated marginal revenue curve:

Assume that a firm is producing at its profit-maximizing level of output.A decrease in fixed cost implies that:

Max Whitley,manager of Whitley Construction,builds new homes in a booming community in the Midwest.Although sales have slowed because of a national recession,it now looks as if the recession is about to end.Max wants to be ready with material,labor,and foremen to meet the demand for housing.Last year,Max built and sold 40 starter homes which is the most popular model.Max thinks that his sales will increase to 50 units over the current year.The going market price for this model (which Max and his numerous competitors have charged)has been $175,000.In addition,Whitley Construction's marginal cost of building this model averages $155,000. (a)Based on these facts,recommend a course of action for Max.

Carefully explain the economic importance of the Lagrange multiplier.How might a manager use it in decision making?

What is the law of demand? How do managers use it in decision-making?

Carefully define marginal analysis,and explain how it is useful in managerial economics.

The following table shows the total revenue (in dollars) and total cost (in dollars) from the production and sale of different units of a product. Table 2-1 -Refer to Table 2-1.What is the marginal profit of the firm from the sale of the 2nd unit of the good?

A firm's total revenue function is given by R = 100 + 10Q + 2Q2,where R = revenue and Q = quantity.Which of the following is true if Q = 10?

Assume that Burger King,a fast food chain,enters into a franchise agreement.The royalty paid to Burger King by the franchisee is calculated as a percentage of the franchisee's revenue.Given that the franchisee faces a downward-sloping demand curve,which of the following is likely to be true?

The demand for a product is given by Q = 600 - 30P,where P = price and Q = quantity.At P = $15,the firm sells _____ units.

Night Timers is a small company manufacturing glow-in-the-dark products.One of the hottest items the engineering department has developed is adhesive tape that can be applied to walls and floors.Night Timers' chief engineer anticipates that the product will be sold in ten-foot rolls.At present,the company's maximum production capacity is 140,000 rolls per year.The engineer believes the cost function to be described by C = $50,000 + 0.25Q,where C is total cost and Q is number of rolls (The high fixed costs represent development cost and tooling to prepare coating equipment).Night Timers' president seeks to establish a price that maximizes profit (since she is the chief stockholder).She thinks that the firm should be able to sell at least 125,000 rolls of tape per year. (a)If Night Timers plans to sell 125,000 rolls per year,what is the necessary price if the firm is to break even? What if it can only sell 100,000?

The following table shows the total revenue (in dollars) and total cost (in dollars) from the production and sale of different units of a product. Table 2-1 -Refer to Table 2-1.What is the marginal revenue of the firm associated with the sale of the 5th unit of the good?

In each case below,find the profit-maximizing level of output.Verify that each output level is a maximum by checking the second derivative. (a) $\pi$ = -50 + 200Q - 10Q²

The following table shows the total revenue (in dollars) and total cost (in dollars) from the production and sale of different units of a product. Table 2-1 -Refer to Table 2-1.What is the profit-maximizing level of output for the firm?

If a firm's profit is given by  = 36Q2 - 360Q - 150,where  = profit and Q = quantity produced,then its optimal output is _____ units.

Suppose that a firm operates in a competitive market where the commodity price is $15 per unit.The firm's cost equation is C = 25 + 0.25Q2,where C = total cost and Q = quantity. (a)Find the profit-maximizing level of output for the firm.Determine its level of profit.