Consider a one-period Keynesian model with no government sector and arbitrary values for investment, autonomous consumption, and the marginal propensity to consume. Specifically, C = Co+ CY : Consumption I = 50 : Fixed investment (a) Derive equilibrium income, consumption, and saving. (b) Assume a government sector is introduced with the sole purpose of maintaining output at level YP, which is a certain value of Y. Derive a policy rule which maps the exogenous variables and Y into government expenditure, assuming no taxes. I (c) Now derive a policy rule that maps the exogenous variables and Y into taxes, assuming no government expenditures. Compare the two policy rules. Why are they different? (d) Assume the government must balance its budget (so G = T). Derive policy rules which map the exogenous variables and YP into taxes and government expenditure. Compare with previous policy rules. Why are they different