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# microbook_3e-page17 - x if denotes a change then if I write...

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Calculus Tricks Calculus is not a pre-requisite for this course. However, the foundations of economics are based on calculus, so what we’ll be discussing over the course of the semester is the intuition behind models constructed using calculus. It’s not surprising therefore that the students who do better in economics courses are the ones who have a better understanding of calculus – even when calculus is not a required part of the course . So if you want to do well in this course, you should learn a little calculus. Ƈ Ƈ Ƈ Many times throughout the course, we’ll be discussing marginalism – e.g. marginal cost, marginal revenue, marginal product of labor, marginal product of capital, marginal utility, marginal rate of substitution, marginal rate of transformation, etc. Whenever you see “marginal …” it means “the derivative of …” A derivative is just a slope. So, for example, let’s say labor is used to produce output x if TP stands for Total Production (quantity produced), x if L stands for Labor input and
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Unformatted text preview: x if ' denotes a change, then if I write: L TP ' ' that’s the change in Total Production divided by the change in Labor. x It’s the slope of the total production function. x It’s the derivative of the production function with respect to labor input. x It’s the marginal product of labor (MPL). So if you understand derivatives, you’ll understand the course material much better. Ƈ Ƈ Ƈ a few preliminaries – exponents You should recall from your high school algebra classes that when you see an exponent, it simply means multiply the number by itself the number of times indicated by the exponent. x x x x 3 ¡ ¡ Now if you divide both sides of the above equation by x: 2 3 x x x x x x x ¡ ¡ But what if you see the something like: x ? Well, that’s simply equal to: 1 x x x x x 1 2 2 2 4 1 8 1 2 2 2 1 2 2 2 2 2 1 4 1 2 2 1 2 2 2 2 1 2 1 2 1 2 2 2 2 2 1 1 2 2 2 2 4 2 2 2 2 2 2 8 4 2 2 2 2 2 2 16 8 2 2 2 2 2 3 1 2 1 1 2 1 3 2 4 3 ¡ ¡ ¡ ¡ ¡ ¡ Page 17...
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