Answer:
Step-by-step explanation:
The consumption function C = 100 + 0.75Y represents the relationship between consumption and disposable income, where C is consumption and Y is disposable income. The equation tells us that for every dollar of disposable income, consumers will spend 75 cents on consumption.
The equilibrium level of output is determined by the intersection of the aggregate demand (AD) and aggregate supply (AS) curves. The AD curve can be derived by adding together the planned consumption, planned investment, planned government spending and planned net exports. In this case, we have:
AD = C + I + G + NX = C + 300 + 600
The aggregate demand equation becomes AD = 100 + 0.75Y + 300 + 600
The aggregate supply equation represents the relationship between the quantity of goods and services produced and the price level, assuming a fixed level of technology and input prices. For this problem, we are assuming that aggregate supply is perfectly inelastic, meaning it does not change with price level.
Given that G = 600 and T = 400, disposable income will be Y = T + Tr(Y-T) = 400 + 0.8(Y-400)
Therefore, we have the equations:
AD = 100 + 0.75Y + 300 + 600
Y = 400 + 0.8(Y-400)
We can now solve for Y by substituting the second equation into the first:
100 + 0.75(400 + 0.8(Y-400)) + 300 + 600 = Y
Solving for Y, we find that the equilibrium level of output is Y = 2200.
In a Keynesian cross diagram, this point would be represented by the intersection of the AD and AS curve.
If government spending (G) and Tax (T) rises by 200, the AD curve shifts to the right. This means that the aggregate demand for goods and services is increasing, which causes an increase in the equilibrium output. The new equilibrium output (Y) will be greater than 2200 and can be found by solving for the new AD function. With the new AD function, the new output Y can be found by using the same steps that you have done above.
It's worth noting that in the above scenario, We are assuming that the aggregate supply is perfectly inelastic, this means that the price level is constant, if the aggregate supply is elastic, then an increase in AD will also lead to an increase in price level, this is known as inflation, which will affect the value of Y.