This is an Intermed Macroeconomic Theory question

Consider the following economy: Aggregate Expenditure E, = C + 1, + G, + X, -M, Consumption Ci = de + be(Y, - T,) Investment I, =a; Y - b; R International Trade M, = bm Y,. X, = X Inflation M= M-I+ VY, Government Expenditure G, = G, T, = T. In this economy, both investment and imports depend on the level of income. Moreover, consump- tion depends on disposable income (income net of taxes) and not just on the level of income as we previously assumed. Use the previous equations to answer the following questions: (a) (7 points) Solve for the equilibrium in the goods market. What is the expenditure multiplier? (b) (7 points) Use the Keynesian Cross to carefully explain the effect of an exogenous shock to the level of expenditure (carefully label the graph). (c) (6 points) Derive the IS curve using deviations from potential output as the endogenous variable. (d) (10 points) Suppose the economy is at its potential output equilibrium with a constant 0.02 inflation rate. Using the full short-run model (IS-MP and Phillips curve), explain what happens to the economy over time if the government decides to increase taxes for two periods. Be sure to include graphs showing how output and inflation respond over time