When money is spent on goods and services, those who receive the money also spend some of it. The people receiving some of the twice-spent money will spend some of that, and so on. Economists call this chain reaction the multiplier effect. In a hypothetical isolated community, the local government begins the process by spending D dollars. Suppose that each recipient of spent money spends 100c% and saves 100s% of the money that he or she receives. The values c and s are called the marginal propensity to consume and the marginal propensity to save and, of course, course, c + s = 1. Let Sn be the total spending that has been generated after n transactions.

Required:
Find an equation for Sn.

Answers

Answer 1

Solution :

If [tex]S_n[/tex] is the total spending generated after n transactions, then [tex]a_n[/tex] is the spending generated during the n-th transaction. Since the government spends D dollars, then [tex]a_1[/tex] = D.

Then the second person will receive D dollars and spend [tex]D_c[/tex] dollars. Therefore, [tex]a_2=D_c[/tex]. The next person will receive [tex]D_c[/tex] dollars, which means they are spending [tex]a_3 = (D_c)c = Dc^2[/tex] dollars. Therefore,

[tex]a_1 = D[/tex]

[tex]a_2=D_c[/tex]

[tex]a_3 = Dc^2[/tex]

[tex]a_4 = (Dc^2)c= Dc^3[/tex]

....

[tex]a_n=Dc^{n-1}[/tex]

∴ [tex]S_n=a_1+a_2+a_3+....+a_n[/tex]

  [tex]S_n = D+Dc+Dc^2+Dc^3+...+Dc^{n-1}[/tex]

  [tex]S_n= D(1+c+c^2+...+c^{n-1})[/tex]

  [tex]S-n=D . \frac{1-c^n}{1-c}[/tex]


Related Questions

how many solutions does this graph have?

Answers

Answer:

one solution

Step-by-step explanation:

It will cross the x-axis one time

In the figure to the right, what is the measure of angle DAC ?

I’m not going to show answer Options because I don’t want anyone to put something random

Don’t put links cs I’m not going to press it <3

Answers

Answer:

47 degrees

Step-by-step explanation:

i am super smart

Solve for all values of x by factoring.'
x2 + 10x + 21 = 0

Answers

Answer:

Step-by-step explanation:

2x+10x=12x

12x=-21

x=-1.75

Answer:

x=-7,-3

Step-by-step explanation:

x2+10x+21

(x+7)(x+3)

x=-7,-3

The 8 red markers in a package account for 4% of all markers in the package. How many markers are in the package?

Answers

Answer:

192 markers

Step-by-step explanation:

if 8 = 4% then 2=1%

so we can assume there are 200markers in the package.

8-200= 192 markers

The complex plane is also known as what?​

Answers

Z-plane could be an answer
the complex plane or z-plane is the plane associated with complex coordinate system, formed or established by the real axis and the perpendicular imaginary axis. ... The complex plane is sometimes known as the Argand plane or Gauss plane. There you go

Multiply.
(-3+2i)(-4+4i)
Write your answer as a complex number in standard form.

Answers

Answer:

4 - 20 i

Step-by-step explanation:

you do stuff and you get 4 - 20 i

an aquarium at the zoo is shaped like a cylinder. it has a height of 4 feet and a base radius of 2.5 feet. the aquarium is being filled with water at a rate of 12 gallons per minute. if one cubic foot is about 7.5 gallons, how long will it take the aquarium to fill? round to the nearest whole minute.

Answers

Answer:

49 minutes

Step-by-step explanation:

Volume

v = πr²h

v = π(2.5²)4

v = 78.5 ft³

--------------------------

Gallons needed

78.5 * 7.5 = 588.75 gallons

----------------------

Time to fill

588.75 / 12 = 49.0625

Rounded

49 minutes

Question 5
A round spinner is divided into five sections, where the sections do not have the same size. Using the measure of the interior angles, the probability of the spinner landing on any individual space on
a spin is calculated and given in the table.
©
1
3
4
5
Section
Probability
2
0.20
0.40
0.20
0.15
0.05
A statistics student is asked to test the integrity of the spinner using a chi-square goodness-of-fit test. What is the minimum number of times the spinner should be spun to conduct this test?

Answers

Answer:

The correct answer is 100

it’s a non calc question

Answers

Answer:

60 Degrees

Step-by-step explanation:

trust me

Find the perimeter X(-2,1) Y(4,3) Z(5,-1)

Answers

Answer:

17.728

Step-by-step explanation:

The radius of a circle is 6.1 millimeters. What is the circle's area?

Answers

[tex]area = \pi \times {r}^{2} \\ area = 3.142 \times {6.1}^{2} \\ area = 3.142 \times 37.21 \\ area = 116.91 {mm}^{2} [/tex]

Listed below are the summary statistics from samples of strontium-90 in baby teeth obtained from twelve Pennsylvania residents and another twelve from New York residents born after 1979. PA NY Mean 147.583 136.417 Stdev 10.6383 5.21289 If we wished to test the claim that the mean amount of strontium-90 from Pennsylvania residents is greater than the mean of New York residents, and can assume that the variances are equal, what is the Test Statistic for this test

Answers

Answer:

9.72

Step-by-step explanation:

s1 = 10.6383 ; s2 = 5.21289

x1 = 147.583 ; x2 = 136.417

n1 = 12 ; n2 = 12

df1 = n1 - 1 = 12 - 1 = 11

df2 = n2 - 1 = 12 - 1 = 11

The test statistic :

(x1 - x2) / sqrt[(sp²/n1 + sp²/n2)]

Pooled variance = Sp² = (df1*s1² + df2*s2²) ÷ (n1 + n2 - 2)

Sp² = ((11*10.6383) + (11*5.21289)) / 22 = 7.926

Test statistic, T* :

(147.583 - 136.417) / √(7.926 * (1/12 + 1/12))

11.166 / √(7.926 * (1/6)

11.166 / √1.321

11.166 / 1.1493476

T* = 9.7150766

Test statistic = 9.72

Find the absolute value
|-7|

Answers

Answer:

7

Step-by-step explanation:

hello :

|-7| = - (-7) = 7

Answer:

the absolute value of l-7l is 7

hope it helps.

A high school student volunteers to
present a report to the administration about the types of lunches students prefer.
He surveys members of his class and records their choices. What type of sampling did the student use?
systematic random sampling
voluntary sampling
• convenience sampling
stratified sampling

Answers

Need this answer for a school paper

Answer:

convenience sampling

Step-by-step explanation:

What is the surface area of the net? *inches squared*

Answers

9514 1404 393

Answer:

  75 in^2

Step-by-step explanation:

The central vertical rectangle (including "ears") has dimensions

  3 in wide by (9+2+2) = 13 in tall

Its area is

  A = LW = (3 in)(13 in) = 39 in^2

__

The two rectangles either side of that have dimensions 2 in by 9 in. The area of each of them is

  A = LW = (2 in)(9 in) = 18 in^2

__

The total net area is the sum of the areas of the parts:

  left rectangle + central rectangle + right rectangle

  = 18 in^2 + 39 in^2 + 18 in^2 = 75 in^2 . . . . surface area of the net

Express 72km/h in meter per sec​

Answers

Answer:

20meter per second is tw correct answer

20 m/s

Step-by-step explanation:

1km/h = 1000m/3600s = 5m/18s

⇒ 72 × 5 ÷ 18 = 20 (m/s)

I’ll give you five Stars right answer only

Answers

Answer:

58

Step-by-step explanation:

i think the answer is 58 please give brainliest

Answer:

(a) 18.5ft

(b) 388.5 ft²

Step-by-step explanation:

(a)

She has 79ft of fence = the perimeter will be 79.

Perimeter of a rectangle = 2(length) +2(width)

79 = 2(21)+2(width)

2(width) = 79 - 42

width = 37/2

width = 18.5ft

(b)

Area of a rectangle = (length)(width) = (21)(18.5) = 388.5 ft²

What is the coefficient in the following expression?
5a– 7

Answers

5 is the Coefficient
the coefficient is 5

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Answers

[tex]\mathcal\pink{The \: answer \: is }[/tex]

only one window has height that is a whole number of centimeters

[tex]\mathcal{HOPE \: IT \: HELPS}[/tex]

[tex]\huge\pink{mark \: as \: brainliest}[/tex]

Given that f(x)=x^3, which equation describes the graph of function g?

a. g(x)=f(x-3)+3
b. g(x)=f(x-3)-3
c. g(x)=f(x+3)+3
d. g(x)=f(x+3)-3​

Answers

Answer:

A or g(x) = f(x − 3) + 3

Step-by-step explanation:

pls help this stuff is so hard to understand

Answers

Answer:

y = 0.5 (2)^x

Step-by-step explanation:

3rd option

you can plug in a coordinate point like (2, 2) to check this.

Hello :D help pls? Thanks
What is the area of this partial circle if the radius is 8 inches long? Leave your answer in terms of pi.

Answers

Answer:201.06

Step-by-step explanation:

Devin has a rectangular vegetable garden. He planted tomatoes in section of the garden with an area of 6 square yards. There were 30 square yards remaining for Devin to plant zucchini. Let g represent the total area of the garden. Which equation models the problem? Solve the equation to find the total area of the garden. g =

Answers

Answer:

g=30y^2+6y^2

Step-by-step explanation:

30 years left after six were taken

Josie makes peanut butter sandwiches. She uses 1/8 cup of peanut butter on each sandwich. How many cups of peanut butter dose she need for 9 sandwiches?

Answers

Answer:

9/8

Step-by-step explanation:

.........................

Answer? ................,,,,,,

Answers

Step-by-step explanation:

what is the formula for the whole surface area of a sphere ?

[tex]a = 4 \times \pi \times {r}^{2} [/tex]

that would give us the whole surface area all 360 degrees or 2×pi arc length all around the sphere.

but we don't need all 360 degrees. we only need the Theta'th (that is the specified angle) part.

in radians the arc length of that angle segment on the "equator" of the sphere

s = r×Theta

and the whole equator circumference is

c = 2×pi×r

so, the Theta'th part is then

r×Theta / 2×pi×r = Theta / 2×pi

we only need that part of the whole sphere surface area, so the formula would look like

[tex]lune = theta \times 4 \times \pi \times {r}^{2} \div (2 \times \pi)[/tex]

=>

[tex]lune = theta \times 2 \times {r}^{2} [/tex]

Two circles are concentric. Two arcs are formed by the same central angle, with arc lengths of 54 and 81 respectively. Which of the following are possible radii for the circles? Select the two correct answers.
23 and 32

12 and 18

32 and 64

40 and 60

14 and 41

Answers

Answer:

i think the answer is 12 and 18

Find the surface area of the cone. Round answer to the nearest tenth.*

Answers

Answer:

628.319 rounded= 628.3

Step-by-step

need ko na po this now

please answer this question

thank you po​

Answers

Answer:

B.

Step-by-step explanation:

URGENT!! PLS HELP 16 students are competing an art contest in how many different ways can students finish first second and third

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Use the compass and ruler to construct the bisector of the angle given below.

Answers

Bisector of the angle is the line that divides the angle into two angles with the same measure. In the image attached, the bisector of the angle is represented by the green line.

The next steps show you how to construct the bisector of the angle from a ruler and a compass.

Draw an arc using the vertex of the angle (O) as the center;Mark the points A and B;Draw an arc using the point (A) as the center;Draw an arc, with the same radius, using the point (B) as the center. This arc should intersect the arc that you draw in the previous step. Draw a line connecting the point C to the vertex O.

Finally, you have the bisector of the angle that is represented by the green line.

Learn more about the bisector of the angle here:

https://brainly.com/question/7288045

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