assume that the mps in an economy is equal to 0.33. the multiplier must be equal to 3.03. you have…

assume that the mps in an economy is equal to 0.33. the multiplier must be equal to 3.03. you have established that the multiplier is 3.03. now assume that autonomous real consumption is $4 trillion. there is no other autonomous spending presently taking place. at what level is consumption equal to real gdp? $ trillion. (round your answer to two decimal places)

assume that the mps in an economy is equal to 0.33. the multiplier must be equal to 3.03. you have established that the multiplier is 3.03. now assume that autonomous real consumption is $4 trillion. there is no other autonomous spending presently taking place. at what level is consumption equal to real gdp? $ trillion. (round your answer to two decimal places)

Answer

Explanation:

Step1: Recall the consumption - GDP relationship

The formula for equilibrium GDP ($Y$) in a simple Keynesian model with only consumption ($C$) is $Y = C$. The consumption function is $C = a+ bY$, where $a$ is autonomous consumption and $b$ is the marginal propensity to consume (MPC). Also, the multiplier ($k$) is related to the marginal propensity to save (MPS) by $k=\frac{1}{MPS}$. Given $k = 3.03$ and $a=4$ trillion.

Step2: Use the multiplier formula to find MPC

Since $k=\frac{1}{MPS}$ and $MPS = 0.33$, and $MPC=1 - MPS$, but we can also directly use the multiplier in the equilibrium - GDP formula. In equilibrium $Y = C$, and $C=a + bY$. Rearranging for $Y$ gives $Y=\frac{a}{1 - b}$. Since $k=\frac{1}{1 - b}$, we know that $Y=k\times a$.

Step3: Calculate equilibrium GDP

Substitute $a = 4$ trillion and $k = 3.03$ into the formula $Y=k\times a$. So $Y=3.03\times4=12.12$ trillion.

Answer:

$12.12$ trillion