Discussion Questions (40 Points) 1. Explain why you want to set the first deriva

Question

Discussion Questions (40 Points)

1. Explain why you want to set the first derivative equal to zero. Answer Here:

2. Provide the two formulas that can be used to calculate the mean and/or the expected value and explain where they are used, Answer Here:

3. When is the null hypothesis a one-sided test and a two-sided test and explain under what conditions is either recognizable in a problem? Answer Here:

4. What market structure are consumers considered to be price-takers and how is the demand curve derived? Answer Here:

Net Benefit is defined at Total Benefit minus Total Cost. Suppose the Total Benefit Function B(Q) is 20 Q – Q and the Total Cost is C(Q) = 4 +2 Q2.

Derive Marginal Benefit-

What level of Q maximizes Total Benefit?-

What level of Q optimizes Total Cost?-

What level of Q optimizes Net Benefit-

Explanation / Answer

The exrema ( i.e. minima and maxima collectively ) is occurs at those points for which first derivative is zero. Hence if we set the first derivative equal to zero, then after solving the equation, the points we get are either minima or maxima.

Formula for calculation of mean is given by = Sum of all observations / Total number of observations

Formula for expected value is given by = sum of ( value of an observation x probability of occurance of the observation )

1st formula of mean is used when we are given some observations are we are to calculate the average value from them.

2nd formula of mean is used when we deal with random variables.

A one-sided test is used if the estimated value departs from a pre-defined value in one direction ( less than or greater than ). Example : Whether price of rice is more than $10 per kilo.

A two-sided test is used if the estimated value may be either more or less than a pre-defined value. Example : Whether a soccerer will score more or less goals than his historical average in today's match.

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