Finding Y* and Starting Comparative Statics Lecture 12 Dr. Jennifer P. Wissink ©2018 Jennifer P. Wissink, all rights reserved. March 7, 2018 1

Announcements-MACRO Fall 2018 All Prelim 1 Testing Locations – Please Check Cornell's Web pages for Building Codes and Building Locations Tuesday 7:30 evening prelim (please arrive no latter than 7:15) Last Names starting with A-J in HLS B14 (Hollister B14) Last Names starting with K-S in KMB B11 (Kimball B11 ) Last Names starting with T-Z in PHL 203 (Phillips Hall 203) People w/accommodation letters for extra time arrive at 5:00pm - URH 202 Early sitters (with no extra time) start at 5:00pm - GSH 142 Wednesday Makeup – note updates to rooms for Wednesday! Makeup (with no extra time) start at 3:00pm – GSH 142 NOW It’s Baker 119!! People w/accommodation letters for extra time start at 1:30pm - URH 301 Reminders Bring a simple calculator to the exam. Bring a watch to the exam. No cell phones. No graphing calculators. No “help” sheets.

Pay-Day! Aggregate output (income) (Y) is a combined term used to remind you of the exact equality between aggregate output and aggregate income. Aggregate income is the total income received by all factors of production in a given period. Aggregate output is the total quantity of goods and services produced in an economy in a given period. 3

The Frugal Economy: Determining Aggregate Desired Expenditures=AEd Pay-Day! What HHs spend out of Y = Consumption (C) How much Firms desire for investment = desired Investment (Id) AEd = C + Id (for now) Note: AEd depends on Y! 5

HHs: Consumption (and Saving) out of Y Assume (for now): A household can do two, and only two, things with its income: Consume (C) a.k.a. consumption Save (S) a.k.a. saving and not savings NOTE the following identities (for now):

HHs:The Consumption Function Determinants of HH consumption include: Aggregate Output (Income) Household wealth Interest rates Households’ expectations about the future Other stuff, too. In The General Theory, Keynes argued that household consumption is directly related to its income. (Lots of other work by others, too.) So...C = f(Y), where Y = Aggregate Output (Income) holding constant... Other stuff, too, liked lagged Y, etc.

HHs: Consumption Function Concepts the subsistence level of consumption the breakeven level of income dis-saving and saving the marginal propensity to consume (MPC) the average propensity to consume (APC) 8

HHs: Saving Function From consumption to saving Recall: C + S = Y, so… S = Y - C Like a see-saw the marginal propensity to save (MPS) the average propensity to save (APS) Note it will always be the case that: MPC + MPS=1 APC + APS=1

A LINEAR Aggregate Consumption Function Derived from the Equation C = 100 + .75Y AGGREGATE INCOME, Y (BILLIONS OF DOLLARS) AGGREGATE CONSUMPTION, C (BILLIONS OF DOLLARS) 100 80 160 175 200 250 400 600 550 800 700 1,000 850

Deriving a Saving Function from a Consumption Function Y - C = S AGGREGATE INCOME (Billions of Dollars) AGGREGATE CONSUMPTION (Billions of Dollars) AGGREGATE SAVING (Billions of Dollars) 100 -100 80 160 -80 175 -75 200 250 -50 400 600 550 50 800 700 1,000 850 150 Y S Y

Firms: Actual versus Desired/Planned Investment Desired or planned investment refers to the additions to capital stock and inventory that are desired or planned by firms. Actual investment is the actual amount of investment that takes place; it includes items such as unplanned changes in inventories. Could be additions Could be depletions

Firms: The Desired Investment Function Desired Investment might depend on: Aggregate Output(Income): Y expected rate of return interest rates technological state of world business expectations animal spirits? attitudes? We will make this part of our model very simplistic for a while... Note: Keynes’ understanding/modeling of investment was so-so

Firms: The Desired/Planned Investment Function For now, we assume that desired/planned investment does not change when income (Y) changes. It is said to be an autonomous variable. a.k.a. exogenous NOTE: Define MPI So..., marginal propensity to invest = 0

Aggregate Desired Expenditure (AEd) for our Simple Linear Frugal Economy

Equilibrium Y* Equilibrium Y* is when: Y* = AEd(Y*) Recall: Aggregate output/income ≡ Y Recall: Aggregate desired expenditure =AEd(Y) = C(Y) + Id Equilibrium Y* is when: Y* = AEd(Y*) Suppose: Y > [C(Y) + Id] So actual aggregate output/income > aggregate desired expenditure So inventory investment is greater than planned/desired So actual investment is greater than planned/desired investment So something will change! Firms will produce less! Suppose: [C(Y) + Id] > Y So aggregate desired expenditure > actual aggregate output/income So inventory investment is smaller than planned/desired So actual investment is less than planned/desired investment So something will change! Firms will produce more!

Equilibrium Y* - Graphically AEd 45° helping line where AEd=Y Y

Equilibrium Y* - Algebraically There is only one value of Y* for which this statement is true. We can find it by rearranging terms: By substituting (C) and (Id) into (AEd) we get: Now impose the equilibrium condition that Y* = AEd(Y*).

Equilibrium Y*- Using A Chart (1) (2) (3) (4) (5) (6) AGGREGATE OUTPUT (INCOME) (Y) AGGREGATE CONSUMPTION (C) DESIRED INVESTMENT (Id) AGGREGATE DESIRED EXPENDITURE (AEd) C + Id UNPLANNED INVENTORY CHANGE Y - (C + Id) EQUILIBRIUM? (Y = AE?) 100 175 25 200 - 100 No 250 275 - 75 400 425 - 25 500 475 Yes 600 550 575 + 25 800 700 725 + 75 1,000 850 875 + 125

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