use the consumption function below to derive the multiplier in the y = c + i + g + x model.\nc = 100 +…

Explanation:

Step1: Express disposable income

Disposable income $Y_d = Y - T$. Assuming $T = 0$ for simplicity, so $Y_d=Y$ and $C = 100+0.6Y$.

Step2: Substitute C into the Y - model

Substitute $C$ into $Y = C+I + G+X$. We get $Y=100 + 0.6Y+I + G+X$.

Step3: Rearrange the equation

Rearrange the equation to solve for $Y$. First, move the terms involving $Y$ to one - side: $Y-0.6Y=100 + I+G + X$. Then $0.4Y=100 + I+G + X$, and $Y=\frac{1}{0.4}(100 + I+G + X)$.

Step4: Identify the multiplier

The multiplier $k$ is the coefficient of the autonomous spending ($100 + I+G + X$). The formula for the multiplier $k=\frac{1}{1 - MPC}$, where $MPC$ (marginal propensity to consume) is 0.6. So $k=\frac{1}{1 - 0.6}$.

Step5: Calculate the multiplier

$k=\frac{1}{0.4}=2.50$.

Answer:

2.50