Answer the following Questions for a Monopoly Firm.

To complete the table you need to know that the Average Total Cost (ATC) of producing 10 units of output is $980 and that the Total Variable Cost (VC) of producing 11 units of output is $10,400.

a) Fill in the missing information above for this Monopoly Firm. Note there are no numbers for MC and MR when Q=0.

b) At which unit of output does Diminishing Marginal Returns start? Please explain your answer.

c) If this firm produces in the Short Run, determine its profit maximizing/loss minimizing output level. Please explain your answer using MC and MR.

d) If this firm produces in the Short Run, determine its profit maximizing/loss minimizing price.  

e) If this firm produces in the Short Run, state its profit maximizing/loss minimizing profit amount.

f) If this firm shuts down in the Short Run, determine its profit maximizing/loss minimizing profit amount. Please explain your answer.

g) What should this firm do in the Short Run in order to maximize its profits/minimize its loss (produce or shut down)? Please explain your answer using numbers.

h) Explain what this firm should do in the Long Run. Why?

Consider the following cost functions:C(Q)=F+cQ,C(Q)=F+Q12, andC(Q)=F+aQ2, whereFrepresents fixed cost. Draw the curves corresponding to average costand marginal cost. Discuss whether any of these production technologies generates anatural monopoly.

Fundamental Toys Inc. is looking to expand its stock portfolio. You receive an urgent text message from Bob: I need you to analyze a Stock X as a possible investment candidate for the company's stock portfolio. The CFO has asked me to make a decision ASAP. I left the data you need on your desk. Fortunately, Excel has the capability of performing regression analysis with built-in algorithms. This frees the analyst from complicated algebraic formulations and data management. The following data has been collected to help you run a linear regression between Stock X and the New York Stock Exchange (NYSE) on which Stock X is traded. Use CAPM as the investment decision model. Data from Bob Historical Rates of Return Year NYSE Stock X 1 (30%) (19.0%) 2 32.5 20.5 3 21.6 16.5 4 (9.8) 0.5 5 7.8 9.7 6 22 20.5 7 33.5 19.8 (Source: Intermediate Financial Management, Brigham and Davies, 10th edition) The NYSE is the independent variable, X-axis, which is the proxy market portfolio. Stock X is the dependent variable, Y-axis. Also, assume a market return (NYSE) of 12%, the risk-free rate of 4% and the market return of Stock X of 7.85%. Submit the following items in to the online drop box. 1.The Excel regression function (the regression equation). 2.The SML constructed from the risk-free rate, beta (slope of the regression function), and the market return provided above. 3.Your conclusion on the stock purchase given your CAPM analysis and the market return of Stock X. Provide support for your decision.

Question 2 The rest of the questions deal with the Motor Trend Car and Sport data from 1974

# It is famous dataset called mtcars comes built in to R. Use the line of code below

# to familiarize yourself with it head(mtcars)

## mpg cyl disp hp drat wt qsec vs am gear carb

## Mazda RX4 21.0 6 160 110 3.90 2.620 16.46 0 1 4 4

## Mazda RX4 Wag 21.0 6 160 110 3.90 2.875 17.02 0 1 4 4

## Datsun 710 22.8 4 108 93 3.85 2.320 18.61 1 1 4 1

## Hornet 4 Drive 21.4 6 258 110 3.08 3.215 19.44 1 0 3 1

## Hornet Sportabout 18.7 8 360 175 3.15 3.440 17.02 0 0 3 2

## Valiant 18.1 6 225 105 2.76 3.460 20.22 1 0 3 1

Question 2a # how many observations are there in this data set?

Question 2b # plot a histogram showing the frequencies of the "cyl" column # as always, make sure the plot is properly labeled.

Question 2c # which car has the highest "qsec"? # which car has the highest "mpg"?

Question 2d The next two questions are great practice for your final project! 1 # plot a scatter plot of mpg vs qsec. Are the variables correlated? If so, are they # negatively correlated or positively correlated?

Question 2e # plot a scatter plot of mpg vs disp. Are the variables correlated? If so, are they # negatively correlated or positively correlated?

For all the requested figures below, use a discrete time range of n = [0,50] on the x-axis. Remember your script should be self-sufficient and run without any errors to receive any points.

You are given a discrete time system (1) below (same system as Homework 5(a)):

(E - 0.2)(E - 0.4)(E - 0.6) y[n] = (2 - 3E) x[n]              (1)

Question 1. Compute the impulse response h[n] of system (1) above, using the recursive solution method. You will not receive any points for using another method. Given the system input x[n] defined by equation (2) below, compute the output yr[n] to the system (1), using h[n] you have just computed and x[n], by discrete convolution. You will not receive any points for computing yr[n] using another method.

x[n] = cos( pi x n/32) u[n]                                    (2)

Display computed yr[n] together with y[n] you have computed in Homework 5(a) on the same figure. Display yr[n] in red circles (‘ro’), and y[n] in blue stars (‘b+’). You are NOT asked to display h[n], do NOT display h[n]. Do not forget to properly label and annotate your figure and follow the time range requirement set on the top of this page. You will not receive full points otherwise.

Note: Use a stem plot, with the help of the built in Matlab function “stem()” in order to properly represent a discrete signal on a figure.

Question 1:

As explained in Lesson 5, data exploration through visualization is important because statistics alone might not tell the entire story. This is best shown by the French statistician Francis Anscombe in 1973 when he presented four sets of data. This data is shown here

Calculate the mean, variance, correlation, and linear regression for each data set (No data partition). Using base R or ggplot2, create a visual representation of this data. What does this visualization show?

Question 2:

• How do you evaluate and compare the developed linear regression models in Question 1? Are there any issues with the models you built?
• Is there any way to improve your linear regression models for Data I, II, and III?

Question 1:

As explained in Lesson 5, data exploration through visualization is important because statistics alone might not tell the entire story. This is best shown by the French statistician Francis Anscombe in 1973 when he presented four sets of data. This data is shown here

Calculate the mean, variance, correlation, and linear regression for each data set (No data partition). Using base R or ggplot2, create a visual representation of this data. What does this visualization show?

Question 2:

• How do you evaluate and compare the developed linear regression models in Question 1? Are there any issues with the models you built?
• Is there any way to improve your linear regression models for Data I, II, and III?

Use α = 0.05 unless told otherwise.

--Everything should be r-code base.

--data set is built-in in r code. Just type in LifeCycleSavings.

--DATA ALREADY EXIST IN R. PLEASE JUST TYPE IN LifeCycleSavings in R.

--DATA IS NOT MISSING

We want to build a multiple regression model to predict sr (the “Savings Ratio”) in the LifeCycleSavings dataset (see ?LifeCycleSavings for more background info).

a. Build a model that uses all the other variables in the data frame as predictors, including all their two-way interactions (I’ll call this the full model). Using an ?-test, does it appear that at least one of the predictors is significant/useful?

b. Regardless of your answer to part a, look at the individual ?-tests for the predictors. Which of the predictors look significant/useful?

c. Use the backwards stepwise procedure to select a reduced (smaller) model from the full model. Which predictors are included in this reduced model?

d. Compare and contrast both the ? 2 s and the adjusted ? 2 s for the full model to the reduced model. What do you observe?

e. Conduct a partial ?-test to compare the reduced model to the full model. Does it appear that we lost anything of value by removing those predictors?

f. In the reduced model, there should be one predictor that looks very insignificant based on its ?-test. Which one is it? And why do you think the stepwise procedure decided to keep it in the model? [Take your best guess on the second part there; we can discuss this idea more.]

***Everything should be in r-code base. Specific explanation with code is needed. thanks in advance.

a) Write an function that finds the independent variable value at which a mathematical function is maximized over a specified interval. The function must accept a handle to a function, and evaluate that function at values ranging from x1 to x2 with an increment of dx. The value returned is the value of x at which the maximum value of f(x) occurs.

Function syntax: xm = xmax(f,x1,x2,dx);

As was the case in the previous problem, this function does not find the true value of x that maximizes f(x). It only identifies the value of x that yields the maximum value of f(x) from among those values of x at which the function is evaluated. How closely this approximates the true maximum point of f(x) will depend on the step size, dx.
Your function should use only basic arithmetic operations and loop structures. You may not use any built-in MATLAB functions (e.g., mean.m, sum.m, max.m, min.m, etc.).
Next, you will investigate how the estimated maximum point varies as a function of dx.

b) Write an m-file, ENGR112_HW6_2.m, in which you define the following as an anonymous function.

?(?)=−?^2+15??+21.843

Define a logarithmically-spaced vector, dx, of 2000 step sizes, from 10-4… 100, at which xmax.m will be used to approximate the maximizing value of f(x) over the interval of 0 ≤ x ≤ 50. Call xmax.m at each value of dx and build a vector of maximizing independent variable values, xm. In

c) Plot the vector of approximate maximizing values as a function of step size using a logarithmic axis for the step size. You should see that the approximation converges as step size gets small enough.

Maurice White is an entrepreneur. He owns his own business. He creates video games using the pictures of his customers as the video game characters. Bobby Brown bought 100 custom built video games from Maurice. To pay for the video games, Bobby issued a note, payable to Maurice. The note states in pertinent part that “I, Bobby Brown, agree that I owe to Maurice White for custom video games, 75,000 dollars to be paid in 10 equal payments of 7,500 dollars each on the first of each month until paid, beginning on November 1 2018.” Bobby signed his name in cursive, but he signed it in the top right hand corner of the document instead of on the signature line. The note is not dated.
**(There are three parts to this question. Read each part carefully and be sure your answer addresses the question presented in each part. YOU DO NOT HAVE TO REPEAT THE QUESTION. JUST PUT AN A, B OR C AT THE BEGINNING OF YOUR ANSWER TO EACH SECTION).**

A. What are the elements of negotiability. (10 pts).

B. Assume that this fact scenario calls into questions at least two of the elements of negotiability. Identify two elements of negotiability that are raised by this fact scenario and explain each element and whether the facts support the two elements you identified. But, in answering this part of the question, do not state your conclusion as to whether or not this is a negotiable instrument. Instead, you should just discuss the two elements you identified. (15 pts).

C. State your conclusion as to whether this is a negotiable instrument. Explain why or why not. You can refer to your answer to the previous parts of this question to support your conclusion. (5 pts).