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

Consider an economy described by the following equations: $$\begin{array}{l} Y=C+I+G \\ C=100+0.75(Y-T) \\ I=500-50 r \\ G=125 \\ T=100 \end{array}$$ where $Y$ is $\operatorname{GDP}, C$ is consumption, $I$ is investment, $G$ is government purchases, $T$ is taxes, and $r$ is the interest rate. If the economy were at full employment (that is, at its natural rate), GDP would be 2,000 a. Explain the meaning of each of these equations. b. What is the marginal propensity to consume in this economy? c. Suppose the central bank's policy is to adjust the money supply to maintain the interest rate at 4 percent, so $r=4 .$ Solve for GDP. How does it compare to the full-employment level? d. Assuming no change in monetary policy, what change in government purchases would restore full employment? e. Assuming no change in fiscal policy, what change in the interest rate would restore full employment?

Transcript

00:01 Once again, welcome to a new problem.

00:06 This time we're doing macroeconomics.

00:11 We're doing macroeconomics and these are the questions we're looking at.

00:18 So think about an economy and the aggregate of the economy involves consumption plus investments, plus government purchases.

00:38 So, you know, y is the gdp, c is the consumption, i is investment, i is investment, and g is government purchases, government parties.

01:01 In this case, c, which is the consumption, is given by this equation, y minus t, where t represents taxes and then the investment equation is 500 minus 50 r where r represents interest interest rate so r stands for the interest rate and then g is 125 remember g is government purchases and the taxes are 100 the we'll say at full employment, at full employment gdp is the same as 2000.

01:56 In part a, explain the meaning of these questions, these questions.

02:12 Part b, we were saying, determine the propensity to consume in the economy and then we were saying the assume that the central bank adjusts money but at hour equals to 4 % remember r is the interest rate determine the gdp compare this to compare this to four employment so you want to compare this to full employment and then in part d at a constant or rather we want to say at varying monetary policy and varying monetary policy what change in government government purchases would restore for employment so what's going to be store for employment and then in part e maintaining the same fiscal policy what variation in interest rate would bring back for those are the questions you're looking at.

04:53 And so we're just going to jump right into these questions.

05:03 Gdp is the same as total monetary value.

05:12 Final goods and services produced in an economy at a specific time period with available available resources.

05:40 These are the available resources that are producing the final goods and substance.

05:48 So aggregate demand, aggregate, demand is the summation of consumption, investment and government expenditure.

06:23 Thus, aggregate demand and then also the same, the consumption, the consumption function relates consumption and disposable income.

06:57 Increasing this income increases, goes to this income up, the consumption and investment function has investment functions, shows the inverse relationship between interest and investment.

07:53 Increasing interest laws, laws investments, decreasing taxes and government spending is assumed.

08:42 So that's part a.

08:45 And then we also have part b, marginal propensity to consume shows changes in consumption based on changes.

09:20 And so the marginal propensity to consume is 0 .75.

09:24 In that c, the interest rate is 4%.

09:31 So to get the gdp, you take the consumption plus investment plus government spending.

09:41 Consumption is $1075, imsd.

09:46 That's investment.

09:47 This is investment.

09:49 So if you go back, you see this is consumption and then this is investment.

09:58 So we're going to plug those formulas into the equation.

10:01 That's consumption and then we have investment affected by interest and then government spending at a constant so this is 725 plus 0 .75 minus 50 times 4 so we want to get 0 .25i minus 50 times 4 so we want to get 0 .25 is 450 is 450 so the gdp which is why this is the gdp becomes the same as 1 ,000 as the gdp.

10:42 And then also we're going to say change in interest produces 1800 gdp...

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