Question 1

War Game, Inc. produces games that simulate historical battles. The market is small but loyal, and War Game is the largest manufacturer. It is thinking about introducing a new game in honor of the sixtieth anniversary of the end of World War II. Based on historical data regarding sales, War Game management forecasts demand for this game to be P = 50 - .002Q, where Q denotes unit sales per year, and P denotes price in dollars. The cost of manufacturing (based on royalty payments to the designer of the game, and the costs of printing and distributing) is C = 140,000 + 10Q.
(a) If the goal of War Game is to maximize profit, calculate the optimal output and price.
(b) If instead the company's goal is to maximize sales revenue, what is its optimal price and quantity?

Accepted Answer

a.The company's profit equation is: π = (50Q – .002Q²) – 10Q – 140,000. To maximize profit, set marginal profit equal to 0. Therefore, Mπ = 40 – .004Q = 0, implying optimal output, Q* = 10,000 units. In turn, P = 50 – (.002)(10,000) = $30 per unit of the game. b.The company's revenue equation is given by: R = P × Q = 50Q - .002Q². To maximize revenue, set marginal revenue equal to 0. Therefore, 50 - .004Q = 0, implying optimal output, Q*= 12,500 units. In turn, P = 50 - (.002)(12,500) = $25 per unit of the game.

Question 2

A firm's total revenue function is given by R = 100 + 100Q - 2Q2. At Q = 10, which of the following is true?

Accepted Answer

A)   The firm's marginal revenue is $80.
B)   The firm's marginal revenue is constant.
C)   The firm's average revenue is $50.
D)   The firm's total revenue is $500.
E)   The firm's marginal revenue is $60. E

Question 3

Are there any types of goods or situations where the law of demand does not hold? Explain.

Accepted Answer

The law of demand states that all other factors held constant, the higher the unit price of a good, the fewer the number of units demanded by consumers and, consequently, sold by firms. For certain goods, a high price is associated with a higher status or luxury, for example, a fancy wine or a designer bag. For such goods, a high price is seen as a sign of exclusivity, which means that the demand for these goods might increase as price increases. These are called Veblen goods.

Question 4

Due to an increase in the price of a competitor's product, the demand for a firm's product increases sharply. How is this most likely to affect the firm's marginal revenue and marginal cost?

Accepted Answer

A)   Marginal revenue will increase but marginal cost will decrease.
B)   Both marginal revenue and marginal cost will not be affected.
C)   Both marginal revenue and marginal cost will increase.
D)   Marginal revenue will not change but marginal cost will increase.
E)   Marginal revenue will increase but marginal cost will not change.

Question 5

The demand for a firm's product is given by the equation: P = 36 - .2Q. The firm's cost equation is given by C = 200 + 20Q.
(a) Determine the firm's optimal quantity and price.
(b) Suppose that the firm’s costs change to C = 100 + 24Q. Determine the new optimal quantity and price. Explain why the results differ from the previous case.

Accepted Answer

The answer of The demand for a firm's product is...

Question 6

The demand for a product is given by Q = 600 - 30P. At P = $15, the firm sells:

Accepted Answer

A)   100 units.
B)   150 units.
C)   300 units.
D)   450 units.
E)   600 units.

Question 7

How will an increase in overhead costs affect the demand and supply curves for a firm? Will an increase in the price of a raw material used in production have the same effect?

Accepted Answer

The answer of How will an increase in overhead costs...

Question 8

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 $275,000. In addition, Whitley Construction's marginal cost of building this model averages $245,000.
(a) Based on these facts, recommend a course of action for Max.
(b) Suppose that the economic boom raises the cost of labor and raw materials, so that the additional cost of a starter house rises to $265,000. What is Max's most profitable course of action? Explain.

Accepted Answer

The answer of Max Whitley, manager of Whitley Construction, builds...

Question 9

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

Accepted Answer

The answer of Carefully explain the economic importance of the...

Question 10

Suppose, at its current output level, a firm's marginal profit is positive. Therefore, to maximize profit, it should:

Accepted Answer

A)   decrease output until marginal profit is zero.
B)   increase output because MR is less than MC.
C)   increase both its output and its price.
D)   increase output because MR is greater than MC.
E)   increase output until it is producing at full capacity.

Question 11

If a firm's demand function is of the form P = a - bQ, what is its marginal revenue equation?

Accepted Answer

A)   MR = a - Q
B)   MR = a - 2bQ
C)   MR = a - 2Q
D)   MR = a - 2b
E)   MR = a + 2bQ

Question 12

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
 $\begin{array} { | c | c | c | c | } 
\hline \text { Price } & \text { Quantity } & \text { Total Revenue } & \text { Total Cost } \
\hline 15 & 1 & 15 & 3 \
\hline 14 & 2 & 28 & 7 \
\hline 13 & 3 & 39 & 12 \
\hline 12 & 4 & 48 & 18 \
\hline 11 & 5 & 55 & 25 \
\hline 10 & 6 & 60 & 33 \
\hline
\end{array}$
-Refer to Table 2-1. What is the marginal revenue associated with the sale of the 5th unit of the good?

Accepted Answer

A)   $55
B)   $8
C)   $7
D)   $48
E)   $4

Question 13

A manufacturing company produces and sells small farm tractors. Its annual fixed costs are $15 million, and its marginal cost per tractor is $20,000. Demand for small tractors is given by: P = 30,000 - Q, where P denotes price in dollars and Q is annual sales.
(a) Find the firm's profit-maximizing output, price, and annual profit.
(b) Assume that agriculture prices fall and the farming sector faces a mild recession. The demand for the small tractors drops to: P = 26,000 – Q. Suppose the recession is only temporary, and demand will recover soon. What price and output adjustment should the firm
make during the recession?

Accepted Answer

The answer of A manufacturing company produces and sells small...

Question 14

Given the total cost equation for a firm, the marginal cost equation can be derived by:

Accepted Answer

A)   dividing total cost by total output.
B)   taking the first derivative of the cost function with respect to quantity.
C)   dividing total variable cost by total output.
D)   subtracting variable cost from the fixed cost at all levels of output.
E)   multiplying the total cost equation by price.

Question 15

Suppose that a firm sells in a competitive market at a fixed price of $12 per unit. The firm's cost function is: C = 200 + 4Q. In this case, how can the firm use marginal revenue and marginal cost to maximize its profit?

Accepted Answer

The answer of Suppose that a firm sells in a...

Question 16

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 + .25Q², where C = total cost and Q = quantity. (a) Find the profit-maximizing level of output for the firm. Determine its level of profit. (b) Suppose that fixed costs increase to $75. Verify that this change in fixed costs does not affect the firm's optimal output.

Accepted Answer

The answer of Suppose that a firm operates in a...

Question 17

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 (b) π = –100 + 300Q – 4Q³

Accepted Answer

The answer of In each case below, find the profit-maximizing...

Question 18

The current manager of a small bicycle shop estimates the demand curve for a child's starter bike to be: P = 80 - 2Q. Costs are given by: C = 200 + 20Q. The former owner of the shop (now retired) urges the manager to keep prices low so as to increase sales and maximize revenue. (The shop pays the former owner 5% of each dollar of earned revenue). If current management follows the former owner's goal, what sales output and price should it set? What strategy would you recommend to maximize profits?

Accepted Answer

The answer of The current manager of a small bicycle...

Question 19

Assume that a firm is producing at its profit-maximizing level of output. A decrease in the price of raw materials used in production is most likely to lead to:

Accepted Answer

A)   an increase in quantity produced at an unchanged price.
B)   a fall in the price of the good and an increase in the quantity produced.
C)   a fall in both the price of the good and the quantity produced.
D)   an increase in both the price of the good and the quantity produced.
E)   a fall in the quantity produced of the good at an unchanged price.

Question 20

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

Accepted Answer

A)   marginal revenue will increase but marginal cost will decrease.
B)   marginal revenue will not change but marginal cost will decrease.
C)   neither average total cost nor marginal cost will change.
D)   neither marginal revenue nor marginal cost will change.
E)   both marginal revenue and marginal cost will decrease.

Exam 2: Optimal Decisions Using Marginal Analysis

A firm's total revenue function is given by R = 100 + 100Q - 2Q². At Q = 10, which of the following is true?

Are there any types of goods or situations where the law of demand does not hold? Explain.

Due to an increase in the price of a competitor's product, the demand for a firm's product increases sharply. How is this most likely to affect the firm's marginal revenue and marginal cost?

The demand for a product is given by Q = 600 - 30P. At P = $15, the firm sells:

How will an increase in overhead costs affect the demand and supply curves for a firm? Will an increase in the price of a raw material used in production have the same effect?

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

Suppose, at its current output level, a firm's marginal profit is positive. Therefore, to maximize profit, it should:

If a firm's demand function is of the form P = a - bQ, what is its marginal revenue equation?

Given the total cost equation for a firm, the marginal cost equation can be derived by:

Suppose that a firm sells in a competitive market at a fixed price of $12 per unit. The firm's cost function is: C = 200 + 4Q. In this case, how can the firm use marginal revenue and marginal cost to maximize its profit?

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 (b) π = –100 + 300Q – 4Q³

Assume that a firm is producing at its profit-maximizing level of output. A decrease in the price of raw materials used in production is most likely to lead to:

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

Exam 2: Optimal Decisions Using Marginal Analysis

A firm's total revenue function is given by R = 100 + 100Q - 2Q2. At Q = 10, which of the following is true?

Are there any types of goods or situations where the law of demand does not hold? Explain.

Due to an increase in the price of a competitor's product, the demand for a firm's product increases sharply. How is this most likely to affect the firm's marginal revenue and marginal cost?

The demand for a product is given by Q = 600 - 30P. At P = $15, the firm sells:

How will an increase in overhead costs affect the demand and supply curves for a firm? Will an increase in the price of a raw material used in production have the same effect?

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

Suppose, at its current output level, a firm's marginal profit is positive. Therefore, to maximize profit, it should:

If a firm's demand function is of the form P = a - bQ, what is its marginal revenue equation?

Given the total cost equation for a firm, the marginal cost equation can be derived by:

Suppose that a firm sells in a competitive market at a fixed price of $12 per unit. The firm's cost function is: C = 200 + 4Q. In this case, how can the firm use marginal revenue and marginal cost to maximize its profit?

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) π\piπ = -50 + 200Q - 10Q2 (b) π = –100 + 300Q – 4Q3

Assume that a firm is producing at its profit-maximizing level of output. A decrease in the price of raw materials used in production is most likely to lead to:

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

A firm's total revenue function is given by R = 100 + 100Q - 2Q². At Q = 10, which of the following is true?

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 (b) π = –100 + 300Q – 4Q³