Consider three economies, A, B, and C

Consider three economies, A, B, and C. Aggregate desired expenditure (AE) in economy A is composed of only consumption expenditures and Investment, in economy B is composed of consumption expenditures, investment expenditures, and government purchases, and in economy C is composed of all those expenditures in Economy B plus net exports expenditures
a. Assume appropriate parametric functions for each component of the AE and right down a parametric system for each economy that defines the economy.
b. Derive the formula for aggregate expenditure function for each economy as a function of autonomous expenditures and induced expenditures.
c. What are the differences in the formula and size of the marginal propensity to spend between the three economies?
d. What are the differences in the formula and size of the simple multiplier between the three economies?
e. If a similar change in autonomous expenditures is introduced in the three economies, in which one you expect a bigger change in equilibrium GDP?
f. Under the same scenario as in part (d), in which economy you expect a bigger horizontal change in the aggregate demand curve?
g. Adding a linear supply curve that is exactly the same for all three economies (in terms of slope and intercepts) to the picture, under the same scenario as in part (d), in which economy you expect a bigger increase in the price level?
h. How does the change in price level in any of these economies depend on the slope of the aggregate supply curve? (i.e., assume a steeper/less steep AS curve.)
i. Explain and graphically show all the changes (including all the steps) in the AE, AD, and AS curves in a 45 degree diagram (for AE) linked with a demand and supply diagram, for an exogenous increase in the autonomous expenditures in economy C.