Problem 4 Suppose an imaginary economy is represented by the following equations

Question

Problem 4 Suppose an imaginary economy is represented by the following equations GDP = C+I = = $100 + 0.SYD 1planned +|Unplanned C 1 |Planned = $200 AEplanned CIPlanned Make sure you show your work in your answers (1) Calculate the income-expenditure equilibrium level GDP Show your work 2) Suppose the level of planned investment spending (Iptanned) drops by 850. What will the new equilibrium GDP be? Show your work. 3) With Iplanned back at the original level of $200, suppose that autonomous consumption spending decreases from $100 to S60. What will the new equilibrim GDP be? Shou your work (4) Calculate the value of the multiplier.

Explanation / Answer

(1) In equilibrium, GDP = Y = C + I

Y = 100 + 0.8Y + 200

(1 - 0.8)Y = 300

0.2Y = 300

Y = 1,500

(2) When I = 200 - 50 = 150,

Y = 100 + 0.8Y + 150

(1 - 0.8)Y = 250

0.2Y = 250

Y = 1,000

(3) C = 60 + 0.8Y

Y = 60 + 0.8Y + 200

(1 - 0.8)Y = 260

0.2Y = 260

Y = 1,300

(4) Marginal propensity to consume (MPC) = 0.8

Multiplier = 1 / (1 - MPC) = 1 / (1 - 0.8) = 1 / 0.2 = 5

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