Question

Problem
Suppose you are given the following macroeconomics data (in million) about an economy:
Aggregate Demand: ??=?+?+?+??
Short-run Aggregate Supply (SRAS): ?=20,000?
❖ ? is the aggregate price level.
❖ Consumption spending: ?=??,???+?.???−??,????
❖ I = $5,000 G = T = $200 X = M = $1,000
A. Find the equation for the AD curve for this economy. (1 point)
B. Find the short-run equilibrium level of real GDP (???) and the aggregate price level (?). (2 points)
C. Assume further that the aggregate production function is: ?=200∗?12, where L is the number of
employed labor. Everything else is constant, find the labor productivity for this economy. (1 point)
D. Because of the corona pandemic, the government decided to increase import by 40% to buy medical goods. Find the new equilibrium price and real output level? Graph all your findings. (3 points)
Hint: Use two decimal numbers only.

Answer 1

AD : Y = C + I + G + NX

NX = N - X

= 1000 - 1000 = 0

Y = 14900 + 0.5YD - 10000P + 5000 + 200 + 0

= 20100 + 0.5(Y -T) - 10000P

= 20100 + 0.5(Y - 200) - 10000P

= 20100 + 0.5Y - 100 -10000P

Y - 0.5Y = 20000 - 10000P

0.5Y = 20000 - 10000P

Y = 40000 - 20000P

2) AS : Y = 20000P

AD = AS

40000 - 20000P = 20000P

40000 = 20000P + 20000P

40000 = 40000P

P = 1

Y = 20000(1)

= 20000

3) Y = 200L^1/2

20000= 200L^1/2

L^1/2 = 100

L = 10000

Labor productivity = 20000/10000

= 2

4) Imports are increased by 40% which means now Imports will be 1000 + 400 = 1400

New equation of AD curve is

Y = 14900 + 0.5(Y - 200) - 10000P + 5000 + 200 + 1000 - 1400

Y = 19700 + 0.5Y - 100 - 10000P

= 19600 + 0.5Y - 10000P

Y - 0.5Y = 19600 - 10000P

0.5Y = 19600 - 10000P

Y = 39200 - 20000P

AD = AS

39200 - 20000P = 20000P

39200 = 20000P + 20000P

39200 = 40000P

P = 0.98

Y = 20000(0.98)

= 19600

1.96 0.98 Р)о ý AD 19600 20,000 39200 40,000 As imports des AD urme shifts down from ADo to ADI , equilibrium price ted from i to 0.98 and equilibrium output alro bed from 20000 to 19600