2. This question asks you to work with a simple short-run macroeconomic model. In this model there are only two types of decision-makers: firms and households (no government and no international considerations). A description of the behaviour of the two groups is that firms choose how much to produce (Y) and how much newly produced capital goods they would like to purchase, and households choose how much of their income they would like to spend and how much they would like to save. Firms produce what they expect to sell. Firms want to purchase 100 (million $) of newly produced capital goods; i.e., I = 100. Households spend as follows: if Y (income) is zero they spend 75 (million $) and if income rises by $1 they spend $0.7; i.e., C = 75 + 0.7 Y. (a) If firms expect to sell 800 and thus produce 800, how much will they actually sell? (b) Do firms end up with inventories they did not intend to have? If so, how much? (c) What is the level of actual investment (as opposed to desired investment)? (d) Find the equilibrium level of GDP (Y). (e) How much do households save when the economy is in equilibrium? (f) Now suppose that households change behaviour: they want to save 25 more (i.e., the savings function shifts up by 25). Find the new equilibrium levels of income (Y) and savings (S) (g) If firms did not anticipate the change in behaviour they would have produced too much. How much too much? What is the actual level of investment spending? (h) In the new equilibrium I = S = 100 which is the same as in the original equilibrium. Why hasnt S increased?