Question : 5.3 Cross Elasticity and Income Elasticity 1) The extent to which : 1239047

5.3 Cross Elasticity and Income Elasticity

1) The extent to which the demand for a good changes when the price of a substitute or complement changes, other things remaining the same, is measured as the

A) income elasticity of demand.

B) cross elasticity of demand.

C) price elasticity of demand.

D) price elasticity of supply.

E) cross income elasticity of demand.

2) The cross elasticity of demand is a measure of how

A) responsive consumers are to changes in the price of a product.

B) responsive suppliers are to changes in the price of a product.

C) demand for a product changes when the price of a substitute or complement changes.

D) total revenue changes when the price of a product changes.

E) demand for a product changes when income changes.

3) If we are trying to determine if two different products are substitutes, complements, or not related at all, we should find the value of the

A) price elasticity of demand for both goods.

B) price elasticity of supply for both goods.

C) income elasticity of demand for both goods.

D) cross elasticity of demand.

E) price elasticity of demand and the price elasticity of supply for both goods.

4) If Microsoft wanted to prove to the Justice Department that its Windows software has many substitutes that personal computer owners can use, Microsoft hopes to find

A) that the demand for Windows’ is inelastic.

B) that the demand for Windows is elastic.

C) a large positive value for the cross elasticity of Windows and other software.

D) a negative income elasticity for Windows.

E) a positive income elasticity for Windows.

5) What is the formula for the cross elasticity of demand? The percentage change in the

A) quantity demanded divided by the percentage change in the price of a substitute or complement.

B) quantity supplied divided by the percentage change in price.

C) quantity demanded divided by the percentage change in price.

D) quantity demanded divided by the percentage change in income.

E) equilibrium quantity demanded divided by the equilibrium quantity supplied.

6) If a 1 percent increase in the price of X increases the quantity demanded of Y by 2 percent, then X and Y are

A) complements and the cross elasticity of demand equals 2.

B) substitutes and the cross elasticity of demand equals 1/2.

C) substitutes and the cross elasticity of demand equals 2.

D) complements and the income elasticity of demand equals 2.

E) normal goods and the income elasticity of demand of each equals 2.

7) The price of coffee rose 40 percent and the quantity of coffee demanded fell by 20 percent. The quantity of doughnuts demanded also fell by 20 percent. From this information, we can conclude that

A) the demand for coffee is elastic.

B) the demand for coffee is unit elastic.

C) coffee is an inferior good.

D) the cross elasticity demand between coffee and doughnuts is -0.5.

E) the income elasticity of demand for coffee is 2.

8) If the price of a movie rises 3 percent and, as a result, the quantity demanded of video rentals increases 6 percent, then the cross elasticity of demand is

A) 2.

B) 1/2.

C) -1/2.

D) -2.

E) 9.

9) Based on data in the table above, use the midpoint method to determine the cross elasticity of demand for ice cream and cake.

A) The cross elasticity is -0.75.

B) The cross elasticity is -1.75.

C) The cross elasticity is -0.83.

D) The cross elasticity is -4.0.

E) The cross elasticity is -1.33.

10) Based on the data in the table above, ice cream and cake are ________ goods.

A) inferior

B) normal

C) substitute

D) complementary

E) Both answers B and D are correct.

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July 1, 2023

Watch video entitled “Module 6 – Discrete-Time Signals in MATLAB”
Work the lab activity below using MATLAB.
Include answers for Problems and include MATLAB coding along with any output plots that support solutions into a Word document entitled “Lab6_StudentID”. Where your student id is substituted in the file name.
Upload file “Lab6_StudentID”.

Activity 1:

A discrete-time system can be described in one of two ways. One is by the unit-pulse response of the system, and the other is by the difference equation. In the first case, if we are given an input and want to find the output, we have to convolve the system response with the input signal. In the second case, we have to solve the difference equation for the output when the input signal is substituted into the difference equation. The result should be the same no matter what approach is used.

A discrete-time system has the following unit-pulse response:

for

Correspondingly, the following difference equation describes the behavior of the system:

Use the Matlab command conv to calculate the response of the system to a unit step input, x[n]=u[n]. Consider . Show what you type into the Matlab command window. Also, submit a plot of the output. Be sure to label your axes.

Matlab Tip: Remember that you can easily get help on a command in Matlab by typing help with the command at the prompt:

EDU>>help conv

Matlab Tip: Also, don't forget that in Matlab when you do certain operations on an array element-by-element, you must precede the operator with a period. For instance, in Matlab, if you define an array n as follows:

EDU>>n=[0:20];

then the first term of the unit-pulse response is written as 0.5.^n

Matlab Tip: Sometimes it is useful to know the size of arrays you have created. This can be done in several ways. For example, you can use the command size:

EDU>> size(n)

ans =

1 21

The size of the array is returned. In this case, the array n has a size of 1 row by 21 columns.

Alternatively, you can switch the display from the Current Directory to the Workspace. Then all current variables and arrays and their sizes are displayed. Just click on Workspace in the upper left corner as indicated below.

Use the Matlab function recur to calculate the response of the system to a unit step input, x[n]=u[n]. Again consider . Show all that you type into the Matlab command window. Submit a plot of the output with the axes labeled.

The Matlab function recur is not a function which comes with Matlab or any of the toolboxes you have installed. Instead, it is a that must be added to your Matlab directory.

The Matlab function recur can be found in a zip file at the Mathworks site at the following location:

http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=2148

Extract the file recur.m to the current directory shown at the top of the Matlab window.

On the other hand, you can copy and paste the script below into a text file like Notepad and save it as recur.m in the current directory shown at the top of the Matlab window.

function y = recur(a,b,n,x,x0,y0);

% y = recur(a,b,n,x,x0,y0)

% solves for y[n] from:

% y[n] + a1*y[n-1] + a2*y[n-2]... + an*y[n-N]

% = b0*x[n] + b1*x[n-1] + ... + bm*x[n-M]

% a, b, n, x, x0 and y0 are vectors

% a = [a1 a2 ... aN]

% b = [b0 b1 ... bM]

% n contains the time values for which the solution will be computed

% y0 contains the initial conditions for y, in order,

% i.e., y0 = [y[n0-N], y[n0-N+1], ...,y[n0-1]]

% where n0 represents the first element of n

% x0 contains the initial conditions on x, in order

% i.e., x0 = [x[n0-M],...,x[n0-1]]

% the output, y, has length(n)

N = length(a);

M = length(b)-1;

if length(y0) ~= N,

error('Lengths of a and y0 must match')

end

if length(x0) ~= M,

error('Length of x0 must match length of b-1')

end

y = [y0 zeros(1,length(n))];

x = [x0 x];

a1 = a(length(a):-1:1); % reverses the elements in a

b1 = b(length(b):-1:1);

for i=N+1:N+length(n),

y(i) = -a1*y(i-N:i-1)' + b1*x(i-N:i-N+M)';

end

y = y(N+1:N+length(n));

To get information on how to use the function, at the Matlab prompt, type:

EDU>>help recur

It might be helpful to change the index of the difference equation such that the highest index is n rather than n+2.

Are your plots the same? If not, why not?

**PLEASE SEE ATTACHMENT**

July 1, 2023

Watch video entitled “Module 6 – Discrete-Time Signals in MATLAB”
Work the lab activity below using MATLAB.
Include answers for Problems and include MATLAB coding along with any output plots that support solutions into a Word document entitled “Lab6_StudentID”. Where your student id is substituted in the file name.
Upload file “Lab6_StudentID”.

Activity 1:

A discrete-time system has the following unit-pulse response:

for

Correspondingly, the following difference equation describes the behavior of the system:

Use the Matlab command conv to calculate the response of the system to a unit step input, x[n]=u[n]. Consider . Show what you type into the Matlab command window. Also, submit a plot of the output. Be sure to label your axes.

Matlab Tip: Remember that you can easily get help on a command in Matlab by typing help with the command at the prompt:

EDU>>help conv

EDU>>n=[0:20];

then the first term of the unit-pulse response is written as 0.5.^n

Matlab Tip: Sometimes it is useful to know the size of arrays you have created. This can be done in several ways. For example, you can use the command size:

EDU>> size(n)

ans =

1 21

The size of the array is returned. In this case, the array n has a size of 1 row by 21 columns.

Use the Matlab function recur to calculate the response of the system to a unit step input, x[n]=u[n]. Again consider . Show all that you type into the Matlab command window. Submit a plot of the output with the axes labeled.

The Matlab function recur is not a function which comes with Matlab or any of the toolboxes you have installed. Instead, it is a that must be added to your Matlab directory.

The Matlab function recur can be found in a zip file at the Mathworks site at the following location:

http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=2148

Extract the file recur.m to the current directory shown at the top of the Matlab window.

On the other hand, you can copy and paste the script below into a text file like Notepad and save it as recur.m in the current directory shown at the top of the Matlab window.

function y = recur(a,b,n,x,x0,y0);

% y = recur(a,b,n,x,x0,y0)

% solves for y[n] from:

% y[n] + a1*y[n-1] + a2*y[n-2]... + an*y[n-N]

% = b0*x[n] + b1*x[n-1] + ... + bm*x[n-M]

% a, b, n, x, x0 and y0 are vectors

% a = [a1 a2 ... aN]

% b = [b0 b1 ... bM]

% n contains the time values for which the solution will be computed

% y0 contains the initial conditions for y, in order,

% i.e., y0 = [y[n0-N], y[n0-N+1], ...,y[n0-1]]

% where n0 represents the first element of n

% x0 contains the initial conditions on x, in order

% i.e., x0 = [x[n0-M],...,x[n0-1]]

% the output, y, has length(n)

N = length(a);

M = length(b)-1;

if length(y0) ~= N,

error('Lengths of a and y0 must match')

end

if length(x0) ~= M,

error('Length of x0 must match length of b-1')

end

y = [y0 zeros(1,length(n))];

x = [x0 x];

a1 = a(length(a):-1:1); % reverses the elements in a

b1 = b(length(b):-1:1);

for i=N+1:N+length(n),

y(i) = -a1*y(i-N:i-1)' + b1*x(i-N:i-N+M)';

end

y = y(N+1:N+length(n));

To get information on how to use the function, at the Matlab prompt, type:

EDU>>help recur

It might be helpful to change the index of the difference equation such that the highest index is n rather than n+2.

Are your plots the same? If not, why not?

**PLEASE SEE ATTACHMENT**

July 1, 2023

Watch video entitled “Module 6 – Discrete-Time Signals in MATLAB”
Work the lab activity below using MATLAB.
Include answers for Problems and include MATLAB coding along with any output plots that support solutions into a Word document entitled “Lab6_StudentID”. Where your student id is substituted in the file name.
Upload file “Lab6_StudentID”.

Activity 1:

A discrete-time system has the following unit-pulse response:

for

Correspondingly, the following difference equation describes the behavior of the system:

Use the Matlab command conv to calculate the response of the system to a unit step input, x[n]=u[n]. Consider . Show what you type into the Matlab command window. Also, submit a plot of the output. Be sure to label your axes.

Matlab Tip: Remember that you can easily get help on a command in Matlab by typing help with the command at the prompt:

EDU>>help conv

EDU>>n=[0:20];

then the first term of the unit-pulse response is written as 0.5.^n

Matlab Tip: Sometimes it is useful to know the size of arrays you have created. This can be done in several ways. For example, you can use the command size:

EDU>> size(n)

ans =

1 21

The size of the array is returned. In this case, the array n has a size of 1 row by 21 columns.

Use the Matlab function recur to calculate the response of the system to a unit step input, x[n]=u[n]. Again consider . Show all that you type into the Matlab command window. Submit a plot of the output with the axes labeled.

The Matlab function recur is not a function which comes with Matlab or any of the toolboxes you have installed. Instead, it is a that must be added to your Matlab directory.

The Matlab function recur can be found in a zip file at the Mathworks site at the following location:

http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=2148

Extract the file recur.m to the current directory shown at the top of the Matlab window.

On the other hand, you can copy and paste the script below into a text file like Notepad and save it as recur.m in the current directory shown at the top of the Matlab window.

function y = recur(a,b,n,x,x0,y0);

% y = recur(a,b,n,x,x0,y0)

% solves for y[n] from:

% y[n] + a1*y[n-1] + a2*y[n-2]... + an*y[n-N]

% = b0*x[n] + b1*x[n-1] + ... + bm*x[n-M]

% a, b, n, x, x0 and y0 are vectors

% a = [a1 a2 ... aN]

% b = [b0 b1 ... bM]

% n contains the time values for which the solution will be computed

% y0 contains the initial conditions for y, in order,

% i.e., y0 = [y[n0-N], y[n0-N+1], ...,y[n0-1]]

% where n0 represents the first element of n

% x0 contains the initial conditions on x, in order

% i.e., x0 = [x[n0-M],...,x[n0-1]]

% the output, y, has length(n)

N = length(a);

M = length(b)-1;

if length(y0) ~= N,

error('Lengths of a and y0 must match')

end

if length(x0) ~= M,

error('Length of x0 must match length of b-1')

end

y = [y0 zeros(1,length(n))];

x = [x0 x];

a1 = a(length(a):-1:1); % reverses the elements in a

b1 = b(length(b):-1:1);

for i=N+1:N+length(n),

y(i) = -a1*y(i-N:i-1)' + b1*x(i-N:i-N+M)';

end

y = y(N+1:N+length(n));

To get information on how to use the function, at the Matlab prompt, type:

EDU>>help recur

It might be helpful to change the index of the difference equation such that the highest index is n rather than n+2.

Are your plots the same? If not, why not?

**PLEASE SEE ATTACHMENT**

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Question : 5.3 Cross Elasticity and Income Elasticity 1) The extent to which : 1239047

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