Quantitative Methods
Miscellaneous
*For profit maximization, a resource should be used until what point?
MVP=MFC
*At the boundary between stages II and III, what is TPP equal to? MPP equal too?
TPP is at its maximum and MPP= zero
*What does the Y=X look like in a Y X coordinate space?
A 45-degree line originating from the origin.
*What does the function Y=2 look like in a Y X coordinate space?
Horizontal line at Y=2
*What is the distance between the smallest and largest measurement of a data set?
The range
*Who developed Calculus?
Sir Isaac Newton
*At the beginning of Stage II, what is the relationship between APP and MPP?
They are equal.
* What is a matrix?
A rectangular array of elements arranged in rows and columns.
*Describe the slope of a demand curve.
It is negative.
*The ratio: Relative change in demand/relative change in price, it is what type of elasticity?
The elasticity of demand at a given price. (Point elasticity of demand)
*The more vertical the supply curve, the ___________ the elasticity.
Greater
Linear Programming
*What do the production possibilities equations tell us?
They define all possible combinations of enterprise that can be produced with the given
or scarce resources.
*What is the shadow price associated with a resource constraint?
The MVP of a one-unit change in a resource. It basically tells you what you would be
willing to pay for one additional unit of a resource
*What is linear programming?
A computational method to determine the best plan or course of action, among many
which are possible, when there are many alternatives for the plan, a specific or numerical
objective exists for it, and resources are limited.
*What are the three quantitative components of a Linear Programming problem?
The objective function, the alternative ways of producing, and resource constraints.
*What is the purpose of a supply-balance (transfer) equation?
It allows output from one activity to be used as an input into another activity. (Ex: Taking
the yield of corn crop & using the corn as feed.)
*What type of activity accounts for unused resources?
A slack activity.
*Which linear programming assumption states that the total usage of each resource equals the
sum used by each activity?
Additivity
*The amount by which profits will decrease if one until of an activity is forced into the solution is
known as what?
The reduced cost
*When is it possible to have multiple optimal solutions to a problem?
If the isoprofit line coincides with one of the boundaries of the feasible solution space.
*The rate of change in the objective function value for a per unit change in a resource is known as
__________________ .
The shadow/dual price
Statistics
*The applications of statistics to business can be divided into two broad areas, what are they?
DESCRIBING large masses of data and making INFERENCES about some set of data
based on sampling.
*What is the difference between quantitative data and qualitative data?
Quantitative data are observations that are measured on a numerical scale. Qualitative
data is nonnumerical.
*What is the difference between X bar and Mu?
X bar is the sample mean; it is used to estimate the population mean. Mu is the
population mean; it is the true mean.
*When is a statistic unbiased?
If its sampling distribution has a mean equal to the parameter it is intended to estimate.
*What is the Central Limit Theorem?
For sufficiently large samples, the sampling distribution of X bar will be approximately
normal.
*What is type I error?
Rejection of the null hypothesis when it is true.
*What is type II error?
Failing to reject the null hypothesis when it is false.
*The general property of the relationship between Type I error and Type II error: as alpha is
_________, beat is ____________.
Decreased (Increased); Increased (Decreased)
*What does a 95% Confidence Interval mean?
That you are 95% sure that the population parameter is within a given interval estimator.
*What two things determine how accurately X bar estimates Mu?
Sample size and variability (spread the data).
Regression
*What is the difference between R square and adjusted R square?
R square equals the percentage of variation explained; adjusted R square equals the
percentage of variance explained.
*What does the use of ordinary least squares for estimating econometric relationships guarantee?
It guarantees that the sum of the square errors in the estimated equation will be minimum.
*What do estimated coefficients indicate?
Each indicates the average units of change in the dependent variable per unit change in
the independent variable for which it is associated.
*In a least squares regression, what is the value of the dependent variable when all independent
variables are equal to zero?
The constant term (B1). [The slope]
*What are the right hand side ranges?
Amounts by which the resource capacities can be increased (decreased) without changing
the activities in the optimum solution.
*What does BLUE stand for?
Best linear unbiased estimator.
*What is an F-test?
A statistical test of the existence of a linear relationship between the dependent variable
and all of the independent variables, with the exception of the intercept.
*What are three of the five assumptions of OLS?
12345-
The expected value of the error is equal to zero.
The equation has linear parameters.
Error terms have the same variance and are not correlated.
The independent variables are non-stochastic.
The number of observations is greater than the number of independent variables.
*The coefficient of multiple determination is equal to the _____________ divided by the total
sum of squares.
The regression sum of squares.
*_________________ refers to a condition in multiple regression analysis when there is a high
level of correlation between independent variables.
Multicollinearity
Calculus
*The slope of any local or global maximum or minimum equals what?
Zero
*Given a function for average cost, how can you determine the average cost per unit?
Divide the function by the number of units.
*When finding a maximum or minimum, what do the second order conditions tell us?
Shape of the curve. Whether it is at a max or a min.
*What is a second order derivative?
It is the derivative if the first order derivative.
*What is an inflection point?
The slope changes from increasing (decreasing) at an increasing rate to increasing
(decreasing) at a decreasing rate.
*The derivative of a function measures what?
The derivative measures the instantaneous rate if change of the function.
*In determining the maximum of a function what are the first order conditions (FOC)?
Set all first order partial derivatives equal to zero.
*The slope of the total revenue curve is equal to what?
Marginal Revenue
*If the graph of a function has two different points of maximization, the higher point is known as
the _______________ max and the lower of the two is known as the ______________ max.
Global, Local
*What is a partial derivative?
Given a function with two or more variables, a partial derivative is the derivative of the
function with respect to one variable and holding all other variables constant.
* Y = AK L
this function is known as?
The Cobb-Douglas Function
* Which variable of a regression output gives the chance that both a and b are statistically
insignificant?
Significance F
* When a curve has two maximum points, what is the higher point called?
Global Maximum
* With regard to minimization, in the second order condition, the function of
X must be....
greater than 0
* State the formula for Price Elasticity:
% change in Q/% change in P
* State 5 Quantitative Methods
Calculus, Statistics, Regression, Linear Programming, and Capital
Budgeting
* If a graph is skewed to the right, in what order will you find the mean and
median starting at the origin moving out?
the mean will be smaller(before) than the median.
* What is the formula for degree of freedom?
n-k-1
* When working a maximization problem the second order conditions should _________.
be less than zero or f'(x)<0
* Linear demand has a constant _______ but not constant __________.
slope, elasticity
* What does MPP stand for?
marginal productivity of product
* Name two properties of a normal distribution.
bell shaped curve, standard normal distribution (mean=0, stdev=1), the sum of two
independent normally distributed variables is also normally distributed
* If the price is in the inelastic portion of the demand curve,
increasing the price will ________ revenue.
Increase
* In moving average predictions, the longer the moving average the
greater the ________.
Smoothing
* To calculate _____ we sum absolute value of deviations and divide by
number of observations.
MAD
* With respect to a completely inelastic demand curve, consumption (does/does not) respond to
price at all.
Does not
* Given an inelastic demand, if the price goes down the change in revenue _______.
decreases
* The Gauss Markov Theorem states that the OLS estimator is the ______ _______ _____
_______.
Best linear unbiased estimator. (BLUE)
* In moving average predictions, the longer the moving average the greater the smoothing.
True
* The adjusted R2 = the ratio of two unbiased estimators.
True
* When two goods are considered to be compliments, their cross-price elasticity is…
Negative
* Of the following three tests, pooled t-test, matched pairs t-test, and 2 sample t-test, which has
the most power and why?
Matched pairs t-test because the samples are dependent (have something in common)
* What is power as it relates to statistics?
The probability of correctly rejecting the null hypothesis
* What is the derivative of total cost?
Marginal Cost
* To be significantly different from zero a p-value must be greater than or less than .05?
# < .05
* An inelastic demand curve is horizontal or vertical?
Vertical
* A random subset of a desired population surveyed in a statistical study:
SAMPLE
* Rate of change of a function
DERIVATIVE, OR SLOPE
* When will mean, median, and mode be equal in a population?
WHEN THE DATA HAS A NORMAL DISTRIBUTION
* What is the null hypothesis associated with the F-statistic?
H0: a = 0 and b = 0
* What is the null hypothesis associated with the t-statistic?
H0: a = 0, H0: b = 0
* What is a significance level?
The percentage of time a true null hypothesis would be rejected by chance.
* Define the income elasticity of demand.
The percent change in quantity with respect to the percent change in income.
* If a problem is minimized, what are to steps to arrive at this conclusion?
Derive First Order Condition FOC: f’(x)=0
Check Second Order Condition SOC: f’’(x)<0
* What is the mean and standard deviation of a Standard Normal Distribution?
Mean= 0
Standard Distribution= 1
* If a curve is skewed right, which of the following would be greater in value: mean or median?
Why?
Mean- outliers pull the mean out to a greater value
* For completely elastic demand, at what price is quantity demanded equal to 0?
At any price greater than p*
* If price decreases, what is the effect on revenue with elastic demand?
It increases.
* What are the measures of central tendency in statistics?
Mean, median, and mode
* What are the two types of discrete random variables?
Logit and probit
* To minimize the sum of residuals is the goal of what?
OLS
* What is y = ÿ0 +ÿ1x +u?
the simple regression model
* F tests are used to test what?
Multiple linear restrictions
* Name the three types of individual risk preferences.
Risk adverse, risk neutral, and risk lover.
* The Markowitz selection procedure is used to do what?
Minimize the trade-off between risk and return.
* Why is the F-test always positive?
Because it’s equal to t squared, and any number squared becomes positive.
* What is the orientation of a completely inelastic demand curve?
Vertical
* In an F test, why is F always positive?
It is the square of t
* What type of product has a cross price elasticity less than zero?
Complement
* Terms: ____________ is the increase in the objective function when the constraint is relaxed by
one unit.
Shadow Value
* The Difference between a Theoretical Model and an Econometric Model is the_______?
Error Term
* Where is total revenue maximized?
* What are the two types of random variables?
Continuous and discrete variables
* What does the Minimum Absolute Deviation (MAD) do?
Minimized the absolute value of the prediction error.
* What does the Second Order Condition tell us?
SOC tells us whether critical values are maximum or minimum for the given
function.
* How does calculus apply to economics?
In determining optimization of resources, elasticity, and in marginal analysis.
* What is a “saddle point” for a multi-variable case and what does it imply?
When the second order condition is not fulfilled the saddle point implies that it
be determined whether the critical values yield maximum or minimum.
can not