(Transcript of audio with descriptions. Transcript includes narrator headings and description headings of the visual content)
(Speaker)
Using the equation from part one, you are asked to find the equilibrium level of GDP.
(Description)
The problem is presented. In an economy without government purchases, transfers, or taxes, and without imports or exports, aggregate autonomous consumer spending is 500 billion dollars, planned investment spending is 250 billion dollars, and the marginal propensity to consume is 0.5. Find the equilibrium value of Y asterisk algebraically.
(Speaker)
To solve for equilibrium, we are going to start with the original equation from part one.
(Description)
Expression is given as follows: AE sub Planned equals 500 billion dollars, plus, 0.5 times YD, plus 250 billion dollars.
(Speaker)
Next we want to combine autonomous consumption, 500 billion dollars, and planned investment spending, 250 billion dollars. And write the equation as planned AE equals 750 billion dollars plus 0.5 times disposable income. Recall from the chapter that equilibrium GDP is found where planned aggregate spending equals disposable income, which we set equal to Y asterisk. Using the equilibrium condition, we are going to set planned aggregate spending equal to disposable income equal to Y asterisk.
(Description)
Equation is given as follows: Y asterisk equals 750 billion dollars, plus, 0.5 times Y asterisk.
(Speaker)
Next, we subtract 0.5 Y asterisk from both sides of the equation. The term is canceled out on the right-hand side and the left-hand side will equal 0.5 Y asterisk. The final step is to divide both sides by 0.5, which yields an equilibrium level of GDP equal to 1500 billion dollars.
(Description)
Algebraic calculation is presented: Y asterisk minus half times Y asterisk, equals, 750 billion dollars plus half Y asterisk minus half Y asterisk. Next, half Y asterisk equals 750 billion dollars. Fraction, half Y asterisk in the numerator, half in the denominator, equals fraction 750 billion dollars over half. And Y asterisk equals 1500 billion dollars.