A country is closed. It has no government sector, and its aggregate price levels and interest rates are fixed. Furthermore, the marginal propensity to consume is constant and the country's consumption function is as follows: C = 200 + 0.75YD, where YD is disposable income and C is consumption. Assume that planned investment equals 75. What is the income-expenditure equilibrium for this country?

The country has closed economy; it means there is no other trading relation with, outside countries. Export imports do not affect the economy of the country, and here is no government interference as mentioned in the question. This is a self sufficient country, its demand fulfilled from inside of the country. So its aggregate price levels and interest rate are fixed. MPC or the marginal propensity to consume indicates whether there is an increase in disposable income or increase in consumption. Here consumption increases equal to the increase in the income.

MPC = ΔC / ΔY which is constant here.

The increase in income in this country is mostly permanent and increases in a fix period of time and proportionately.

C = 200 + 0.75 YD (YD is disposable income), Y=75, GDP = $900

The economy achieves it's equilibrium level when supplies meets demand or the GDP is equals to it's total expenditure. MPC is a fraction between 0 and 1, MPC means a change in consumption brings the change in YD. here the MPC is equals to MPS which means the change in saving bring by the change in disposable income. All income here saved or consumed. So the change in income equals to the change in consumption or saving.

MPC + MPS = 1

So the average propensity to consume is proportionate to income which is spend on consumption. APC = C / YD. And the average proportionate to save is equals to income saved APS = S/YD. so here APC + APS = 1. The increase in production or price leads to the increase in the total value of output, that is the equilibrium condition.