Consider the macroeconomic model:Y = C + I ————— (2)C = a + b√Y

Consider the macroeconomic model:

Y = C + I ————— (2)

C = a + b√Y

—————(3)

Here: Y is national income, I is fixed investment that does not depend upon C or Y,and a > 0 and b > 0 are parameters. C stands for total consumption by all agents in the economy and, as can be seen from the second equation above, depends upon the level of national income.

(a) Solve for Y . This is called the equilibrium level of income in the

economy

Hint: It might help if you define Z = √Y so that Z^2 = Y. You should end up with a quadratic equation to solve.