(Transcript of audio with descriptions. Transcript includes narrator headings and description headings of the visual content)
(Speaker)
In this question you are going to calculate the change in government purchases needed to close a recessionary or inflationary gap.
(Description)
Calculate the change in government purchases of goods and services necessary to close the recessionary or inflationary gaps in the following cases. Assume that the short-run aggregate supply curve is horizontal, so that the change in real GDP arising from a shift of the aggregate demand curve equals the size of the shift of the curve.
(Speaker)
Assume the short-run aggregate supply curve is horizontal throughout the problem. In the first part, we are given real GDP equals 100 billion dollars.
(Description)
Real GDP equals 100 billion dollars, potential output equals 160 billion dollars, the government collects 20 percent of any change in real GDP in the form of taxes, and the marginal propensity to consume is 0.75. On the Figure there is a graph of aggregate demand. Horizontal axis corresponds to real GDP. Vertical axis corresponds to aggregate price level. The demand line AD1 passing through points on two axes at the same distance from the origin is plotted. Two additional straight lines are plotted: LRAS line parallel to y-axis at 160 billion dollars real GDP and SRAS line parallel to x-axis at the aggregate price level P1 crossing demand line at (100 billion dollars, p1).
(Speaker)
Potential output equals 160 billion dollars. The government collects 20 percent of any change in real GDP in the form of taxes. And the marginal propensity to consume is 0.75. To help visualize the problem, we have provided a graph showing the economy is currently in a recessionary gap.
(Description)
On the Figure there is a graph of aggregate demand AD1, LRAS and SRAS. The demand line AD1 passes through points on two axes at the same distance from the origin. LRAS line is parallel to y-axis at 160 billion dollars real GDP, and SRAS line is parallel to x-axis at the aggregate price level P1 crossing demand line at (100 billion dollars, p1). The interval between the intersection points of SRAS with AD1 and LRAS correspondingly is labeled "Recessionary gap".
(Speaker)
The appendix outlines the details for calculating the multiplier when taxes depend on the real GDP. In this problem the government collects 20 percent of any change in real GDP in the form of taxes. In the equation, 20 percent is the value of t.
(Description)
Multiplier equals fraction: 1 in the numerator, 1 minus MPC times (1 minus t) in the denominator.
(Speaker)
You can see the multiplier has been modified to capture the effect of a tax rate in the problem. The term MPC times 1 minus t reflects the addition of a tax rate in this problem. Previously households would spend a fraction of every additional dollar, which we call the MPC. Now households first have to pay a portion as taxes. For every dollar earned the household keeps 1 minus t. Now the household only spends MPC times 1 minus t. You will notice that if the tax rate equals 0, then the multiplier will reduce to the simple multiplier introduced earlier.
(Description)
if t=0, then: Multiplier equals fraction, 1 in the numerator, 1 minus MPC times (1 minus 0) in the denominator, equals fraction, 1 in the numerator, 1 minus MPC in the denominator.
(Speaker)
If the MPC is 0.75 and the tax rate is 20 percent, we can solve the equation. Doing so, you will find the multiplier equals 2.5.
(Description)
Multiplier equals fraction, 1 in the numerator, 1 minus 0.75 times (1 minus 0.20) in the denominator, equals fraction, 1 in the numerator, 1 minus 0.6 in the denominator, equals 2.5.
(Speaker)
The next step is to find the size of the recessionary gap. If equilibrium GDP is 100 billion dollars and potential output equals 160 billion dollars, the economy has a recessionary gap of 60 billion dollars. Next, to determine how much to increase government spending, we simply divide the output gap by the multiplier. Doing so yields 60 billion divided by 2.5, or 24 billion dollars.
(Description)
Recessionary Gap equals 160 billion dollars minus 100 billion dollars, equals 60 billion dollars. Delta Government Purchases equals 60 billion dollars divided by 2.5, equals 24 billion dollars.
(Speaker)
If government purchases increase by 24 billion dollars, real GDP will increase by 60 billion dollars. The AD line will shift to the right. And the recessionary gap will close.
(Description)
Delta Y asterisk equals 2.5 times 24 billion dollars equals 60 billion dollars. On the Figure there is a graph of aggregate demand. The demand line AD1 passing through points on two axes at the same distance from the origin is plotted. Two additional straight lines are plotted: LRAS line parallel to y-axis at 160 billion dollars real GDP and SRAS line parallel to x-axis at the aggregate price level P1 crossing demand line at (100 billion dollars, p1). New aggregate demand line AD2 parallel to original and shifted to the right crossing intersection point of LRAS and SRAS is plotted. Arrows indicate the right shift with delta G equal to 24 billion dollars. And gap is closing with delta Y equal to 60 billion dollars as indicated by the arrow.