1. What is the purpose of setting the first derivative equal to zero in the opti

Question

1. What is the purpose of setting the first derivative equal to zero in the optimization process?

2. Suppose you are optimizing a function with the highest power of 3, describe how you would determine whether a max, min, or inflection point. Provide an example.

3. Suppose the price and quantity equilibrium is below the price and quantity which maximizes total revenue, what strategy would you use for the firm. Assume that the demand curve is downward sloping.

4. Suppose the firm is operating in the inelastic portion of its demand curve, what strategy would you use to increase the firm's total revenue.

5. Interpret the results of the Jarque-Bera Statistic for a series' descriptive statistic is 0.5140?

Explanation / Answer

1).

First, all first-order partial derivatives must equal zero when evaluated at the same point, called a critical point. If we are considering a function z with two independent variables x and y, then the three-dimensional shape taken by the function z reaches a high or low point when evaluated at specific values of x and y; these values are determined by setting the first derivatives equal to zero, and then solving the resulting system of equations for the two variables.

Let's try an example. Given the following function, start by setting first derivatives equal to zero:

Note: Not possible to answer above all questions in a single question because, system accepting only 65,000 characters.

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