Full version Qrb501 - Week One Problems

Qrb501 - Week One Problems

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WEEK ONE PROBLEMS

QRB501

McConnell & Brue Text

Chapter 7: Study Question 12

The following table shows nominal GDP and an appropriate price index for a group of selected years. Compute real GDP. Indicate in each calculation whether you are inflating or deflating the nominal GDP data.

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Chapter 8: Study Question 2

Suppose an economy's real GDP is $30,000 in year 1 and $31,200 in year 2. What is the growth rate of its real GDP?

[(31,200 – 30,000) / 30,000] * 100 = 4.00%

Assume that population is 100 in year 1 and 102 in year 2. What is the growth rate of GDP per capita?

(30,000 / 100) = 300.00

(31,200 / 102) = 305.88

[(305.88 – 300.00) / 300.00)] * 100 = 1.96%

Chapter 8: Study Question 11

If the CPI was 110 last year and is 121 this year, what is this year's rate of inflation?

[(121 – 110) / 110] * 100 = 10.00%

What is the "rule of 70"?

The rule of 70 is a mathematical approximation of the number of years it will take a given measure to double, given a fixed annual percentage increase. To calculate the rule of 70, divide the annual percentage of increase into the constant 70.

How long would it take the price level to double if inflation persisted at the following rates?

a) 2%

70 / 2 = approximately 35 years

b) 5%

70 / 5 = approximately 14 years

c) 10%

70 / 10 = approximately 7 years

Chapter 20: Study Question 2

Graph the accompanying demand data, and then use the midpoint formula Ed to determine price elasticity of demand for each of the four possible $ price changes. What can you conclude about the relationship between the slope of a curve and its elasticity? Explain in a non-technical way why demand is elastic in the northwest segment of the demand curve and inelastic in the southwest segment.

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For down-sloping straight-line demand curves, price-elasticity in highest in the upper left portion of the curve and becomes more inelastic as the curve slopes downward to the right. This is a function of the elasticity coefficient formula. In the upper left portion of the curve, percentage change in quantity is large relative to percentage change in price. In the lower right portion of the curve, the reverse is true; percentage change in price is large relative to percentage change in quantity.

Chapter 22: Study Question 7

A firm has fixed costs of $60 and variable costs as indicated in the table on the following page. Complete the table. Check your calculations by referring to question 4 at the end of Chapter 23.

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a) Graph total fixed cost, total variable cost, and total cost. Explain how the law of diminishing returns influences the shapes of the variable-cost and total-cost curves.

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The law of diminishing returns assumes that technology is fixed and methods of production do not change. As production begins to increase, variable costs, and by extension total costs, increase at a decreasing amount. As production grows beyond four units in this scenario, variable and total costs begin a more rapid rise due to diminishing returns.

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b) Graph AFC, AVC, ATC, and MC. Explain the derivation and shape of these four curves and their relationship to one another. Specifically, explain in non-technical terms why the MC curve intersects both the AVC and the ATC curves at their minimum points.

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The Average Fixed Cost graph is a function of total fixed cost divided by units produced. The graph is negatively skewed and proceeds asymptotically as production increases. At a value of one unit produced, Average Fixed Cost = Average Total Cost = $60.00.

The Average Variable Cost graph is a function of total variable cost divided by units produced.

Since total variable cost is subject to the law of diminishing returns, the same is true in the average variable cost curve. Average variable costs initially decrease, as production becomes more efficient and average product increases. After the fourth unit of production, the law of diminishing returns becomes a factor, causing average variable costs to begin to rise.

The Average Total Cost graph is the sum of average fixed cost plus average variable cost. The shape of the graph is a hybrid of the average fixed cost and average variable cost graphs. At any point on the X-axis, the plot for average total cost will equal the sum of average fixed cost plus average variable cost.

The Marginal Cost graph is a function of change in total cost divided by change in quantity produced. Marginal cost is the added cost of producing one additional unit of production, or the savings in not producing one additional unit. The graph decreases until the fourth unit of production, and then increases rapidly, as marginal cost is tied to total cost and is thus subject to the law of diminishing returns.

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The Marginal Cost graph intersects the Average Total Cost graph and the Average Variable Cost graphs at their minimum points. As long as the cost of producing one additional unit remains less than average total cost, the average total cost continues to fall. When marginal cost finally exceeds average total cost, average total cost begins to rise in response. The same effect applies to the relationship between marginal cost and average variable cost.

c) Explain how the location of each curve graphed in question 7b would be altered if (1) total fixed cost had been $100 rather than $60 and (2) total variable cost had been $10 less at each level of output.

If fixed cost had been $100 rather than $60:

- The Average Fixed Cost graph would retain its shape but be positioned $40 higher at one unit of production. It would proceed asymptotically to the right.

- The Average Variable Cost graph would be unchanged.

- The Average Total Cost graph would retain its shape, be $40 higher at one unit of production, and always be the sum of average fixed cost and average variable cost.

- The Marginal Cost graph is a function of average total cost, and would retain its shape but be positioned higher in the plot due to the increase in average total cost.

If total variable cost had been $10 less at each level of production:

- The Average Fixed Cost graph would be unchanged.

- The Average Variable Cost graph would be $10 less at each level of production.

- The Average Total Cost graph would retain its shape, be $10 lower at one unit of production, and always be the sum of average fixed cost and average variable cost.

- The Marginal Cost graph is a function of average total cost, and would retain its shape but be positioned lower in the plot due to a decrease in average total cost.

Marshall, McManus, & Viele Text

Chapter 3: Study Question E3.6

a) Firm D has net income of $27,900, sales of $930,000, and average total assets of $465,000. Calculate the firm's margin, turnover, and ROI.

Margin = $27,900 / $930,000 = .03

Turnover = $930,000 / $465,000 = 2.00

ROI = .03 * 2.00 = .06 = 6.0%

b) Firm E has net income of $75,000, sales of $1,250,000, and ROI of 15%. Calculate the firm's turnover and average total assets.

($75,000 / $1,250,000) * (1,250,000 / x) = .15

($75,000 / x) = .15

$75,000 = .15x

($75,000 / .15) = x

x = $500,000

Average total assets = $500,000

Turnover = ($1,250,000 / $500,000) = 2.50

[Check work: .06 * 2.50 = .15]

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c) Firm F has ROI of 12.6%, average total assets of $1,730,159, and turnover of 1.4. Calculate the firm's sales, margin, and net income

Sales = $1,730,159 * 1.4 = $2,422,222.6

Net income

(x / $1,730,159) = 12.6

x = (12.6 *$1,730,159)

x = $21,800,003.40

[Check work: ($21,800,003.40 / $1,730,159) = 12.6]

Net income = $21,800,003.40

Margin

Margin = ($21,800,003.40 / $2,422,222.60) = 9.00

[Check work: 9.00 * 1.40 = 12.6]

Horngren Text

Chapter 2: Study Question 2-B2

1) Given: selling price per unit, $20; total fixed expenses, $5000; variable expenses per unit, $15.

Find: break-even sales in units.

Unit sales price: $20

Unit variable cost: $15

Unit contribution margin: $ 5

Break-even sales in units = $5000 / $5 = 1000 units

2) Given: sales, $40,000; variable expenses, $30,000; fixed expenses, $7500; net income, $2500.

Find: break-even sales in dollars.

Total sales: $40,000 100%

Variable expenses: $30,000 75%

Contribution margin percentage: 25%

Total fixed expenses = ($7500 - $2500) = $5000

Break-even sales in dollars = $5000 / .25 = $20,000

3) Given: selling price per unit, $30; total fixed expenses, $33,000, variable expenses/unit, $14.

Find: total sales in units to achieve a profit of $7000, assuming no changes in selling price.

Unit sales price: $30

Unit variable cost: $14

Unit contribution margin: $16

Target sales volume in units = ($33,000 + $7000) / $16 = 2500 units

4) Given: sales, $50,000; variable expenses, $20,000; fixed expenses, $20,000; net income, $10000. Assume no change in selling price. Find net income if activity volume increases 10%.

Total sales: $50,000

Variable cost plus 10%: $22,000

Fixed cost: $20,000

Total cost: $44,000

Income = $50,000 – 44,000 = $6000

5) Given: selling price per unit, $40; total fixed expenses, $80,000; variable expenses per unit, $30. Assume that variable expenses are reduced by 20% per unit, and the total fixed costs are increased by 10%. Find the sales in units to achieve a profit of $20,000, assuming no change in selling price.

Unit sales price: $40

Unit variable less 20%: $24

Unit contribution margin: $16

Fixed cost plus 10%: $88,000

Target sales volume in units = ($88,000 + $20,000) / 16 = 6750 units