Assume that that tax revenues (T) are proportional to income (Y). That means if the tax rate is equal to t, then we have

T = tY.

Also, consumption (C) and investment (I) functions are given as the following:

C = a + b (Y - T) [where a and b are constant]

I = c - dr. [where c and d are constant, and r is the interest rate]

Part a. (10 Marks) Find the expression of the government purchase multiplier. (Use derivative)

Part b. (10 Marks) What will happen to multiplier if tax rate increases? What will happen to multiplier if MPC increases?