Question

In macroeconomic theory, total consumption expenditure on goods and services, C,

Decimals
ANSWERED
asked 2021-09-21

In macroeconomic theory, total consumption expenditure on goods and services, C, is assume to be a linear function of national income, I. The table gives the values of C and I for 2004 and 2009 in country A(in billions of dollars).
a. Find the formula for C as a function of 1.
b. The slope of the linear function is called the marginal propensity to consume. What is the marginal propensity to consume for country A from 2004-2009?
a. FInd the formula for C as a function of I.
\(\displaystyle{C}=?\)
\(\begin{array}{|c|c|} \hline \text{Year}&2004&2013 \\ \hline \text{Total consumption (C)}&$8,289&$10,086\\ \hline \text{National income(f)}&$9,938&$12,027\\ \hline \end{array}\)

Expert Answers (1)

2021-09-22
Let \(\displaystyle{\left({x}_{{{1}}},{y}_{{{1}}}\right)}\) be the total consumption and Nation income is 2004.
Let \(\displaystyle{\left({x}_{{{2}}},{y}_{{{2}}}\right)}\) be the total consumption and Nation income in 2009.
Since, we have to write C as a linear function of I, \(\displaystyle{x}_{{{1}}}=\${8},{289},{y}_{{{1}}}=\${9},{938}\) and \(\displaystyle{x}_{{{2}}}=\${10},{086},{y}_{{{2}}}=\${12},{027}\).
From this state we arrive at the point (8,289,9,938)(10,086,12,027)
To find slope using two point formula:
\(\displaystyle{m}={\frac{{{y}_{{{2}}}-{y}_{{{1}}}}}{{{x}_{{{2}}}-{x}_{{{1}}}}}}\) ...(1)
Slope of the linear function is \(\displaystyle{y}={m}{x}+{b}\) ...(2)
Substitute \(\displaystyle{m}={0.9070}\) in (2)
\(\displaystyle{y}={0.9070}{x}+{b}\) ...(3)
To find b:
Substitute \(\displaystyle{m}={0.9070}\) and \(\displaystyle{x}=\${8},{289},{y}=\${9},{938}\) in (3)
\(\displaystyle{9},{938}={0.9070}{\left({8},{289}\right)}+{b}\)
\(\displaystyle{b}={2419}\)
Substitute \(\displaystyle{m}={0.9070}\) and \(\displaystyle{b}={2419}\) in (3)
\(\displaystyle{y}={0.9070}{x}+{2419}\)
Express C as an exact linear function of I.
\(\displaystyle{C}={0.9070}{I}+{2419}\)
Part b):
From part a) slope of the linear function is 0.9070.
Hence, the marginal propensity to consume for country A from 2004-2009 is $0.9070.
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