Consider an economy described by the following equations: Y...

Consider an economy described by the following equations: $$ \begin{aligned} Y &=C+I+G \\ C &=100+0.75(Y-T) \\ I &=500-50 r \\ G &=125 \\ T &=100 \end{aligned} $$ where $Y$ is GDP, $C$ is consumption, $I$ is investment, $G$ is government purchases, $T$ is taxes, and $r$ is the interest rate. If the economy were at full

Consider an economy described by the following equations:
$$
\begin{aligned}
Y &=C+I+G \\
C &=100+0.75(Y-T) \\
I &=500-50 r \\
G &=125 \\
T &=100
\end{aligned}
$$
where $Y$ is GDP, $C$ is consumption, $I$ is investment, $G$ is government purchases, $T$ is taxes, and $r$ is the interest rate. If the economy were at full

Transcript

00:01 In the final question of chapter 34, we have a set of equations that describes the state of the economy, of the macroeconomy.

00:09 And in part a, we need to explain the meaning of each of these equations.

00:13 All right.

00:13 So let's start with the first equation, the main one, which is the national income identity.

00:19 Y equals c plus i plus g, which simply means that aggregate output or national income, y, or gdp, you can call gdp, is equal to its cost.

00:30 Components, consumption plus investment plus government spending.

00:34 Usually you might have seen net exports added to this equation as imports minus exports or exports minus imports.

00:45 But here we're dealing with a closed economy so there's no international trade.

00:49 All right.

00:50 The second equation is a consumption function, which reads consumption equals to some fixed level of consumption.

00:57 You can think of it up subsistence level of consumption, which is, equal to 100 plus 0 .75 times y minus t let's think about what y minus t represents it is income minus taxes so it's disposable income this is again a very simple consumption that says a simple function that says a consumption is equal to some fixed level times a parameter that describes how strongly consumption reacts to changes in income or taxes so if we think about a this represents a linear function that has an intercept of 100 and and it's upward sloping with the slope of the line equal to 0 .75.

01:44 So it denotes a positive relationship between consumption and income or a negative relation between consumption and taxes.

01:51 All right, the third equation is an investment function, an aggregate investment function, which states that investment equals to some fixed level of investment, which is equal to 500, minus 50 times the interest rate.

02:06 Again, here, this is a linear function with a negative slope, which is equal to minus 50.

02:14 And we can think about this minus 50 as the sensitivity of investment to the interest rate, which means that as the interest rate goes up, invest by 1%.

02:25 Investment will go down by 50 units.

02:27 So there's a negative relation between investment and the interest rate.

02:30 As we already know.

02:32 And finally, we've been given some parameter values for government spending and taxes, which are usually exogenously given in a model.

02:40 All right.

02:41 Part b asks us to determine what is the marginal propensity to consume in this economy? well, margin propensity to consume has something to do with consumption, right? so if we look at the consumption function, what would that be? we know that the mpc is the slope of the consumption function.

03:01 And here, here, the stop is 0 .75.

03:04 So the mpc is going to be equal to 0 .75 or 2 or 3 4ths.

03:10 And this means, of course, that when income increases by one unit, consumption will increase by 0 .75 units.

03:17 Or accordingly, if taxes are reduced by one unit, again, consumption will increase by 0 .75 units.

03:28 So it's the responsiveness of consumption to changes in disposable income, in this case...

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