- December 4, 2020

Introduction to Macroeconomics New York University

Marc Lieberman Fall, 2014

Supplemental Problem Set #6

Note: To learn more about solving these types of problems, attend one of the recitations Friday Oct 31 or Monday Nov 3.

Consider the following numerical example of the simple Keynesian model:

C = 420 + .6Y_{D}

I^{p} = 90

G = 100

T = 100

NX = 50

where

Y_{D} = disposable income (Income minus net taxes)

T = net taxes

Assume that all of the above variables are measured in billions of dollars and refer to *real *variables (i.e. adjusted for any inflation that might be happening). For example, the equation for consumption tells us that real consumption spending is equal to $420 billion plus 60% of real disposable income, where disposable income is also measured in $billions).

SHOW ALL WORK, and circle your final numerical answers.

1. What is the value of the marginal propensity to consume (MPC) in this model?

2. Draw a careful graph showing aggregate expenditure. Then, draw in the 45-degree line, and illustrate the equilibrium real GDP.

[Make your graph large so you can add to it in subsequent questions. If it helps you, you can first draw in a line for C, then one for C + I^{p}, then a line for C + I^{p} + G, then a final line for aggregate expenditure (C + I^{p} + G + NX] If you want to get the most out of this graph-drawing exercise, use graph paper.]

3. Solve for the equilibrium GDP algebraically. (Hint: use the equilibrium condition Y = C + I^{p} + G + NX, and don’t forget that Y_{D} = Y ‑ T.)

4. In equilibrium, what is the value of consumption spending? (Hint: use the value you found for Y, then solve for Y_{D}, then C.) Use this number to verify that the sum of C, I^{p} and G + NX in equilibrium equals the value for equilibrium GDP you obtained above.

5. Suppose the production function for the economy is:

Y = (10)[(L)(K)(R)]^{½} (i.e., 10 times the square root of L x K x R)

where:

L = employment (number of millions of workers)

K = capital stock ($ trillions)

R = land (billions of acres)

and suppose that K = 25 and R = 18. In equilibrium, how many people will be employed?

[Hint: Plug in the data you’ve been given, and the equilibrium level of output you found above, into the production function equation, then solve for the number of workers (L) it takes to produce that equilibrium output level.]

6. Suppose full‑employment in the economy requires that 98 million people are working. What is “potential” or “full‑employment” GDP?

[Hint: Using the data you’ve been given, use the production function equation to solve for the output level we *would *be producing at full employment.]

7. At the equilibrium GDP, is there a recessionary or inflationary gap? Show the gap on your graph and give it’s numerical value.

8. Suppose business firms decided that, for the good of the economy, they would all start hiring more workers and producing more output. As a result, employment actually rises to 98 million workers and output rises to the full‑employment level of GDP you found in 6. above. What would happen to aggregate inventories in the economy? (Give a *numerical *answer). On your graph, label this hypothetical change in inventories that *would* occur *if *the economy *were *operating at full‑employment). How would business firms respond to this change in inventories?

9. What is the value of the “expenditure multiplier” in this economy?

10. Use the value of the expenditure multiplier to answer the following question: what level of planned investment spending (I^{P}) would create an equilibrium at full‑employment GDP, instead of the equilibrium we are currently stuck at in this problem set?