a) In a closed economy, consider the aggregate income is , consumption () is the

sum of autonomous consumption and the part of consumption that depends on the

disposable income, fixed investment is , and government spending is . If the

country's tax rate is , then what is the amount of private savings and public

savings? From the national income identity for the above economy, show that the

national savings is the sum of private savings and public savings, and is identical to

the fixed investment.

Note: If you derive the identity from lump-sum taxes, you have to estimate the

amount of lump-sum tax given the information above.