Suppose the economy of a country has the following consumption function:

C = 100 + 0.8Y - 0.1r

where C is consumption spending, Y is national income, and r is the interest rate.

a) Derive the equation for the savings function in this economy.
b) Suppose that investment spending is I = 400 - 100r. Find the equation for the equilibrium level of national income.
c) Suppose the government decides to increase its spending by 100 units. Find the new equilibrium level of national income.
d) Calculate the marginal propensity to consume (MPC), the marginal propensity to save (MPS), and the marginal propensity to import (MPI) in this economy.

Show all your calculations and provide detailed explanations for each part of the question.