Consider three economies, A, B, and C. Aggregate desired expenditure (AB) 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 these 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