Economics Principles I New York University
Marc Lieberman Fall, 2012
Answers to Problem Set #6
1. MPC is .6
2. (see graph below.)
3. Equilibrium condition is: Y = C + Ip + G + NX
Substitute for C, Ip, G and NX:
Y = 420 + .6(Y‑T) + 90 + 100 + 50
Y = 420 + .6(Y‑100) +90 + 100 + 50
Y = 420 + .6Y ‑ 60 + 90 + 100 + 50
Y ‑ .6Y = 600
.4Y = 600
Y = 1500
4. In equilibrium, Y = 1500, and C = 420 + .6(Y‑T), so in equilibrium, C = 420 + .6(1500 ‑100 ) = 1,260. Aggregate expenditure = C + Ip + G + NX = 1260 + 90 + 100 + 50 = 1500 (same as equilibrium Y, so it checks)
5. Y = (10)[L(25)(18)]½
1500 = (10)(450L)½
150 = (450L)½
(150)2 = 450L
22,500 = 450L ===> L = 22,500/450 = 50 (or 50 million workers)
6. If LFE = 98, then YFE = (10)[(98)(25)(18)]½ = 2100.
7. There is a recessionary gap of 2,100 ‑ 1500 = 600.
8. If business firms did produce the full‑employment GDP of 2100, this would create an aggregate income of 2100 as well, which would result in C = 420 + .6(2100 – 100) = 1620, while we would still have Ip = 90, G = 100, and NX = 50. Total aggregate expenditure would be 1620 + 90 + 50 + 100 = 1860. But with Y = 2,100, aggregate expenditure would fall short of output by 2,100 – 1,860 = 240, which would be the amount inventories would increase over the period. Firms would respond by decreasing output. Thus, full‑employment output cannot be sustained in this economy without some “help” from the government.
9. The expenditure multiplier = 1/(1‑MPC) = 1/(1‑.6) = 2.5.
10. To achieve full employment, we need GDP to increase from 1500 to 2100, an increase of 600. The expenditure multiplier is 2.5. We use the formula, DY = DIP x (multiplier), substituting 600 for DY and 2.5 for the multiplier, giving us 600 = DIP x (2.5). Then solve for DIP, as follows: DIP = 600 / 2.5 = 240. So, the necessary rise in planned investment spending is $240 billion. Since IPwas originally $90 billion, the required new level of IP is $90 + $240 = $330 billion.
Graph for answers to 2, 7 and 8 on next page:
