4. Consider the following multiplier model: ? = ? ? ? ? = ? ??? ?? ?? = ? ? Where Y, C, I and G are defined as usual, C is a Keynesian consumption function. Imagine that the Government funds its purchases by levying a proportional tax on income so that ? = ??, where ? is the tax rate. Investment in the economy is fixed at ? = ?0. a) Write down the expression for equilibrium output. That is, solve this for output Y. b) How much will output increase if the government increases its expenditure (G) by 1? That is, find the government expenditure multiplier. c) Assume ?0 = 12, ? = 15, ? = 10, ??? = 0.75, ? = 0.2. What is the equilibrium income? d) What is the government expenditure multiplier given the numbers in c)? e) What happens to equilibrium income if tax rate increases to 0.3? Is the outcome consistent with the intuition