CH1 Notes

CH1 Notes - Example Consider the previous example y = x 6x...

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3 | P a g e A.6 Maximization of Multivariable Functions In many situations a dependent variable will be related to two or more independent variables. In this case in order to find the maximum or minimum we take the partial derivatives of the function in terms of each independent variable, and set each of these derivatives equal to zero. Example: Consider the previous example y = - x² + 6x + 1 Derivative: dy/dx = 6 – 2x Second Derivative: d²y/dx² = - 2 The second derivative is negative, so we know that y achieves a maximum when x=3. Example: Suppose we are interested in the maximizing the profit of a firm, where profit equals: π = 13Q₁ - 2(Q₁)² + Q₁Q₂ + 8Q₂ - 2(Q₂)² Derivative: π / Q₁ = 13 - 4Q₁ + Q₂ = 0 Derivative: π / Q₂ = Q₁ + 8 - 4Q₂ = 0 From here we must solve two equations and two unknowns to find the values of Q₁ and Q₂ that maximize the function. b Q₁ = 4 and Q₂ = 3 are the values that maximize the firm’s profit function.
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4 | P a g e 1. Analyzing Economic Problems 1.1 Why Study Microeconomics? Review: What is Economics? Economics is often described as the science of constrained choice . This stems from the following logic: Recall from your previous economics classes that economics is concerned mainly with the allocation of limited resources to satisfy unlimited human wants. h Human Wants are all the goods and services that individuals desire (food, shelter and clothing). Clearly human wants are unlimited. h Production of goods and services requires resources (labor, managerial talent, capital, raw materials). Resources are said to be scarce because their supply is limited. h
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This note was uploaded on 05/09/2009 for the course ECON 410 taught by Professor Codrin during the Spring '07 term at UNC.

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CH1 Notes - Example Consider the previous example y = x 6x...

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