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# Quantitative Reasoning Excercises

1. 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.
Year Nominal GDP Billions, Price Index (1996 = 100) Real GDP, Billions
1960 \$ 527.4 22.19 \$____
1968 911.5 26.29 \$____
1978 2295.9 48.22 \$____
1988 4742.5 80.22 \$____
1998 8790.2 103.22 \$____

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

3.If the CPI was 110 last year and is 121 this year, what is this year's rate of inflation? What is the "rule of 70"? How long would it take for the price level to double if inflation persisted at (a) 2, (b) 5, and (c) 10 percent per year?

4.Graph the accompanying demand data, and then use the midpoint formula for Ed to determine price elasticity of demand elasticity of demand for each of the four possible \$1 price changes. What can you conclude about the relationship between the slope of a curve and its elasticity? Explain in a nontechnical way why demand is elastic in the northwest segment of the demand curve and inelastic in the southeast segment.
Product Price Quality Demanded
\$5 1
4 2
3 3
2 4
1 5

5. A firm has fixed costs of \$60 and variable costs as indicated in the table on the following page. Complete the table and check your calculations by referring to question 4 at the end of Chapter 23.
1.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.
2.Graph AFC, AVC, ATC, and MC. Explain the derivation and shape of each of these four curves and their relationships to one another. Specifically, explain in nontechnical terms why the MC curve intersects both the AVC and the ATC curves at their minimum points.
3.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.

Total Product TFC TVC Total Cost AFC AVC ATC Marginal Cost
0 \$___ \$0 \$___ \$___ \$___ \$___ \$___
1 ___ 45 ___ ___ ___ ___ ___
2 ___ 85 ___ ___ ___ ___ ___
3 ___ 120 ___ ___ ___ ___ ___
4 ___ 150 ___ ___ ___ ___ ___
5 ___ 185 ___ ___ ___ ___ ___
6 ___ 225 ___ ___ ___ ___ ___
7 ___ 270 ___ ___ ___ ___ ___
8 ___ 325 ___ ___ ___ ___ ___
9 ___ 390 ___ ___ ___ ___ ___
10 ___ 465 ___ ___ ___ ___ ___

6. ROI analysis using DuPont model.
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.
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.
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.

7. Basic CVP Exercises
Each problem is unrelated to the others
1. Given: Selling price per unit, \$20; total fixed expenses, \$5,000; variable expenses per unit, \$15.
Find break-even sales in units.

2. Given: Sales, \$40,000; variable expenses, \$30,000; fixed expenses, \$7,500; net income, \$2,500.
Find break-even sales in dollars.

3. Given: Selling price per unit, \$30; total fixed expenses, \$33,000; variable expenses per unit, \$14.
Find total sales in units to achieve a profit of \$7,000, assuming no change in selling price.

4. Given: Sales, \$50,000; variable expenses, \$20,000; fixed expenses, \$20,000; net income,
\$10,000. Assume no change in selling price; find net income if activity volume increases 10%.

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 expenses are increased
by 10%. Find the sales in units to achieve a profit of \$20,000, assuming no change in selling price.

#### Solution Preview

Please refer attached files for better clarity of tables and formulas. Graphs are missing here.

Solutions:

1.

Year Nominal GDP Billions, Price Index (1996 = 100) Real GDP, Billions
1960 \$527.40 22.19 527.40*100/22.19=\$2,376.75 Inflate
1968 911.5 26.29 911.5*100/26.29=\$3,467.10 Inflate
1978 2295.9 48.22 2295.9*100/48.22=4,761.30 Inflate
1988 4742.5 80.22 4742.5*100/80.22=\$5,911.87 Inflate
1998 8790.2 103.22 8790.2*100/103.22=\$8,515.99 Deflate
We deflate GDP when prices rise (CPI is more) and inflate GDP when prices fall (CPI is less) compared to a base year.

2.
Growth in real GDP=(31200-30000)/30000=4%
Real GDP per capital in year 1 =30000/100=\$300
Real GDP per capital in year 2 =31200/102=\$305.8824
Growth in Real GDP per capita=(305.8824-300)/300=1.96%

3.

Rate of inflation for year(t)= [{Price level(year t)-Price level (year t-1)}/ Price level (year t)]*100

Inflation = [{CPI(this year)-CPI(last year)}/CPI (last year)]*100
=[(121-110)/110]]*100=11*100/110=10%

"Rule of 70" ...

#### Solution Summary

There are 7 problems. Solution to these problems explains the concepts of CPI, Real GDP, Inflation, Marginal Analysis, Du Pont model and CVP Analysis. Graphs and tables are included where needed.

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