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 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. (See chapter 23 if you find it difficult.) 7. Consider a typical aggregate demand and supply curve of an economy operating at its long-run equilibrium. a. Express the condition for long-run equilibrium and graphically show the long- run equilibrium of this economy in an AD-AS diagram. b. Explain and graphically show how a positive AD shock affects the short-run equilibrium of this economy. How do the price level and rGDP change in the short term as a result? c. Does the positive AD shock result in a recessionary gap or an inflationary gap? Explain and clearly indicate the size of the gap. d. What does this short-term output gap imply in terms of the rate of usage of factors of production compared to the normal rate indicated by potential output: higher rate of usage or lower than the normal rate? e. How does rate of usage of factors of production you indicate in part (d) impact the price of factors of production? f. What does the impact you identify in part (e) imply in terms of the unit cost of production for firms? g. What does the impact you identify in part (f) imply in terms of the profits of firms if the price of their product, quantity of production, and amount of factors of production they use for production remain constant? h. To remain as profitable as before, firms should increase their price at all levels of production level in response to the impact on their unit-cost of production that you identified in part (f). What does it mean in terms of the position of the aggregate supply curve?