Relationship between the rate of change of output and

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Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach
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Chapter 3 / Exercise 20
Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach
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relationship between the rate of change of output and the rate of investment is known as the acceleratorprinciple.3.A second important determinant of investment is cost. Because capital equipment usually lasts a numberof years and is expensive, firms typically finance investment projects by borrowing. Therefore, interest ratesare an important cost associated with investment. An additional cost factor related to investment is thecorporate taxlevied on firms by the government. Taxes decrease profits, thereby decreasing the attractiveness ofinvestment projects. Alternatively, investment tax credits, given by the government, may encourage firms toexpand investment.4.Investment is the most volatilecomponent of aggregate demand. One of the reasons behind the volatilityof investment is the importance of expectationsin determining the level of investment spending. Sinceinvestment projects, by their very nature, depend upon the future, corporate leaders spend a great deal of timeand effort trying to establish accurate forecasts of the business climate and the economy.5.The investment demand curve relates the interest rate to the level of investments. It is downward-slopingand can shift up or down as the level of output in the economy, tax rates, and expectations about the futurechange.Figure 22-16.Figures 22-7 and 22-9 from the text are reproduced here as Figures 22-1 and 22-2. Note how the pattern ofconsumption spending is fairly stable and predictable. As disposable income in the economy increases, so doesconsumption spending. It almost looks like a one to one relationship. In fact, if the savings rate in the
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Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach
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Chapter 3 / Exercise 20
Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach
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366economy is five percent, the slope would be 0.95. Investment spending, on the other hand, is indeed morevolatile. As the rate of growth – of course, you remember that growth is always measured in realterms – inGDP increases, so does the rate of change in real investment. However, the relationship is not as stable as theone between consumption and disposable income. When the rate of growth in GDP varies between two andfour percent, the rate of change in investment varies from slightly less than zero to over ten percent!Figure 22-2V. HELPFUL HINTS1.If you are unfamiliar with graphs, slopes, and plotted lines, head back immediately to the appendix toChapter 1.2.There is a precise accounting relationship between disposable income, consumption, and saving. Aftertaxes have been paid, households are left with disposable income. This money is either consumed orsaved—there are no other choices. Any two of these three terms will always, by definition, determine the valueof the third.3.Economists are very fond of marginal analysis and margin means change(especially small change).Change, you should recall, is also how we measure a line’s slope (changein Yaxis over changein Xaxisbetween two points). So, margin is the same thing as slope. This concept is very useful for economists. Forexample, from microeconomics: the slopeof total cost is marginalcost, and the slope

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