# Preparation course Msc Business & Econonomics

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1 Preparation course Msc Business & Econonomics The simple Keynesian model Tom-Reiel Heggedal BI August 2014 TRH (BI) Keynes model August / 19

2 Assumptions Keynes model Outline for this lecture: Go through/repeat Keynes model Baseline short-term assumptions: 1 One type of good (which can be a basket of goods). 2 A given price level (short time horizon), i.e. very rigid prices. 3 A closed economy (no trade) 4 Supply is flat; firms produce what is demanded. In this model investments and government spending are exogenous. TRH (BI) Keynes model August / 19

3 The composition of GDP Notation: Y - GDP C - Private consumption: Goods/services purchased by the consumer. I - Investments: Firms and people s purchases of durable goods. G - Government spending: Purchases of goods and services by the government. T - The level of taxation. X - Exports IM - Imports What we are going to find is Y. What determines GDP in the short run in a simple (closed) economy? So far we have some accounting identities, but no way to understand how changes in variables relate to each other. TRH (BI) Keynes model August / 19

4 Aggregate demand in the model We ll find the demand in this simple model. Total expenditure in this economy is by definition given by the sum C + I + G. Denote Z the aggregate demand in the economy. Aggregate demand is in a sense a different word for aggregate expenditure. It is Z = C + I + G where C + I + G is the subcomponents in demand. In equation (??), no X or IM, since no trade. Aggregate demand in an open economy, Z = C + I + G + NX, where NX = X IM. TRH (BI) Keynes model August / 19

5 Aggregate demand, cont. In Z = C + I + G, the investments I and government consumption G are exogenous. Though, we need assumptions to determine the consumption level. Assume that C is a general function of private disposable income, Y D, A behavioral assumption. Y D is further defined as, where Y I is income. C = C (Y D ) (1) Y D = Y I T, (2) TRH (BI) Keynes model August / 19

6 Aggregate demand, cont. 2 Specifying C as a linear function, C = c 0 + c 1 Y D = c 0 + c 1 (Y I T ), where c 0 > 0 and 0 < c 1 < 1. (3) c 0 and c 1 are parameters (to describe aggregate behavior). c 1 is the marginal propensity to consume. Natural to assume that 0 < c 1 < 1. c 0 is the autonomous consumption demand. TRH (BI) Keynes model August / 19

7 Aggregate demand, cont 3 To complete the goods market model, we have assumed: Fixed level of investments I = I. T and G are policy tools, determined outside the model. I, T and G are exogenous variables (while C and Y are endogenous). Combining we now have an equation for aggregate demand that we can work with Z = C + Ī + G = Z = c 0 + c 1 (Y I T ) + Ī + G TRH (BI) Keynes model August / 19

8 Equilibrium condition Supply Y produced in the model is assumed to be "flat". In other words, supply is very elastic. The equilibrium condition in the model is that supply is equal to demand Y produced = Z (4) This equilibrium condition when the supply curve is flat, is basically assuming that firms pridoduce whatever is demanded at the current prices. Can only be justified in the short term, for limited changes in demand. TRH (BI) Keynes model August / 19

9 Accounting identities Remember, that all production value (GDP) is income: by definition production is equal to income Y produced = Y I and last that GDP can be defined from either the production or income side so we can anytime write Y = Y produced = Y I TRH (BI) Keynes model August / 19

10 Solving the model: Analytical vs graphical solution Equilibrium: The values of the endogenous variables (Y and C) for a given set of exogenous variables (and parameters) and given the assumptions and equations specified hold Comparative statics: The magnitude of Y and/or C, given some I, T, or G ( is the change in value). In addition, analyze the effects of c 0 and c 1. Analytical and graphical solution: Analytical solution: Mathematical representation (by deriving and differentiating the equilibrium). Graphical solution: Graphical representation (by drawing and shifting curves). TRH (BI) Keynes model August / 19

11 Analytical solution Merge the different equations into one equilibrium equation, and solve for the endogenous variables Y and C. Solve the two equations 1 Demand/expenditure given by: Z = c 0 + c 1 (Y I T ) + I + G. 2 Supply (and the equilibrium condition): Y P = Z. 3 given the identity Y = Y produced = Y Income. This implies solving Y = Z Y = c 0 + c 1 (Y T ) + Ī + G TRH (BI) Keynes model August / 19

12 Analytical solution cont. Isolating Y on the LHS gives the equilibrium expression Y = 1 1 c 1 [ c0 + I + G c 1 T ]. (5) [ c0 + I + G c 1 T ] : Autonomous spending (exogenous). 1 1 c 1 : The multiplier. Find C! TRH (BI) Keynes model August / 19

13 The graphical approach The two main components in the model: 1 Demand/expenditure given by: Z = c 0 + c 1 (Y I T ) + I + G. 2 Supply (and the equilibrium condition): Y P = Z together with 45 degree line that shows production is equal to income Y P = Y I TRH (BI) Keynes model August / 19

14 The graph TRH (BI) Keynes model August / 19

15 Multiplier effects An example: Find the effects of T = 1 on Cand Y. From (2) and (3): C = c 1 Y D = c 1 (Y T ) = c 1 ( Y T ) = c 1 (0 ( 1)) = c 1 ( Hence, if c 1 = 0.6, then C = 0.6. But, this can not be an equilibrium, because the process goes on: C = Z = Y. Moreover: Y = C = Z = Y = C = Z = Y =... These endogenous adjustments, called multiplier effects, is complicating the analysis! TRH (BI) Keynes model August / 19

16 Analyzing the model: An example An example: A shift in I......equal to I. What will be the effects for Y and C? And how does the equilibrium (Y and C) depend on c 1? TRH (BI) Keynes model August / 19

17 1: Solving the problem analytically Using the equilibrium expression (5), we get Because 0 < c 1 < c 1 Y = 1 1 c 1 I > I. Y = 1 1 c 1 I. > 1, it must be that Example: c 1 = 0.5 = 1 c 1 1 = = 2. Hence, Y = 2 I (> I ). Hence, in equilibrium: Shifts in the autonomous spending a more than one-for-one effect on Y. The multiplier ( 1 1 c 1 ) is determined by the value of c 1. TRH (BI) Keynes model August / 19

18 2:Show in graph TRH (BI) Keynes model August / 19

19 3: describing the analysis Intuition for results. Important to describe the analysis in words. In this framework, what is an, short run, argument for reducing austerity in the EU? TRH (BI) Keynes model August / 19

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