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 $100 c \%$ and saves $100 s \%$ 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, $c+s=1$(a) Let $S_{n}$ be the total spending that has been generated after $n$ transactions. Find an equation for $S_{n}$(b) Show that $\lim _{n \rightarrow \infty} S_{n}=k D,$ where $k=1 / s$. The number $k$ is called the multiplier. What is the multiplier if the marginal propensity to consume is $80 \% ?$ Note: The federal government uses this principle to justify deficit spending. Banks use this principle to justify lending a large percentage of the money that they receive in deposits.
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
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 $100 c \%$ and saves $100 s \%$ 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, $c+s=1$
(a) Let $S_{n}$ be the total spending that has been generated after $n$ transactions. Find an equation for $S_{n}$
(b) Show that $\lim _{n \rightarrow \infty} S_{n}=k D,$ where $k=1 / s$. The number $k$ is called the multiplier. What is the multiplier if the marginal propensity to consume is $80 \% ?$ Note: The federal government uses this principle to justify deficit spending. Banks use this principle to justify lending a large percentage of the money that they receive in deposits.
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