- November 30, 2020

Economics Principles I New York University

Marc Lieberman Fall, 2012

Supplemental Problem Set #6

Do the problem set on your own, but do *not *turn it in. Check your answers against the answers that will be posted by the suggested due date listed on the Aplia home page. Please withhold any *specific *questions about this problem set until *after *you’ve had a chance to review the answers. Then, if you are still confused or troubled about something, either (1) see me during office hours, or (2) email one of the TAs to set up a meeting. [TA contact info is on the Aplia home page, in the “Course Materials” section, in the document titled “TA & Recitation Info”]

Note: Recitation this week will cover problems similar to these.

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

T = net taxes

Assume all variables are measured in billions of dollars (e.g., consumption spending is measured in $billions and is equal to $420 billion plus 60% of 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. Using graph paper, 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).

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 (millions of people)

K = capital stock ($billions)

R = land (millions of acres)

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

[Hint: use the production function and the data you’ve been given to solve for the number of workers (L) it takes to produce the equilibrium output level you found in 3. above.]

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

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 employ 98 million workers and begin to produce the full‑employment GDP. 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 at?