1) Consider the national income model with the following equations.

Y=C+I+G_0, I = f(, r) , C= 5C₀ where Y is income, I is investment, c is consumption, G₀ is government expenditure, measures the level of investor confidence, and r is the interest rate. f is a non-linear function.

i) Using differentials, find dY/d and dY/dr.

ii) Suggest (economically meaningful) conditions on the functions f so that dY/d is positive and dY/dr is negative.

iii) Using a diagram with Y on the horizontal axis and aggregate expenditure on the vertical axis, depict how an exogenous change in and r affect the equilibrium level of income Y.