MPC stands for Marginal Propensity to Consume, which is the change in consumption (C) due to a change in income (Y).
In this model, consumption is a function of income and taxes, and investment, government spending, and net exports are all constant.
The consumption function is given by:
C = 280 + 0.5(Y - T)
Substituting the expression for taxes:
C = 280 + 0.5(Y - 0.6Y)
C = 280 + 0.5(0.4Y)
C = 280 + 0.2Y
The equation for total output (Y) is:
Y = C + I + G + X
Substituting the expressions for C, I, G, and X:
Y = (280 + 0.2Y) + 200 + 300 + 100
Simplifying:
Y = 880 + 0.2Y
0.8Y = 880
Y = 1100
Now that we have found the value of Y, we can calculate the value of MPC as the change in consumption (C) due to a change in income (Y):
MPC = ΔC / ΔY
Assuming a small change in income, we can calculate the change in consumption as the derivative of the consumption function with respect to income:
ΔC = dC/dY * ΔY
Taking the derivative of the consumption function:
dC/dY = 0.2
Substituting the values:
ΔC = 0.2 * ΔY
Therefore, the MPC is 0.2.