DERIVING THE MULTIPLIER ALGEBRAICALLY IN A CLOSED ECONOMY Recall that our consumption function is: C = a(Y – T) where a is the marginal propensity to consume. In equilibrium: Y = a(Y-T) + I + G Now we solve this equation for Y in terms of I , G, C & T. Y a(Y T ) I G C
DERIVING THE MULTIPLIER ALGEBRAICALLYThis equation can be rearranged to yield: Y − aY = I + G – aT Y(1 - a) = I + G - aTWe can then solve for Y in terms of I , G & T by dividingthrough by (1 − a): 1 Y ( I G aT ) 1 a
DERIVING THE MULTIPLIER ALGEBRAICALLYNow look carefully at this expression and think aboutincreasing I by some amount, ΔI, with a held constant.If I increases by ΔI, income will increase by 1 Y I 1 aBecause a ≡ MPC, the expression becomes Y 1 I 1 MPC
DERIVING THE MULTIPLIER ALGEBRAICALLYThe multiplier is 1 1 MPCFinally, because MPS + MPC ≡ 1, MPS is equal to 1 −MPC, making the alternative expression for themultiplier 1/MPS•marginal propensity to consume (MPC) That fraction of achange in income that is consumed, or spent.•marginal propensity to save (MPS) That fraction of a change inincome that is saved.
The government purchases multiplier Definition: the increase in income resulting from a $1 increase in G. In this model, the govt purchases multiplier equals Y 1 G 1 MPCExample: If MPC = 0.8, then An increase in G causes income to Y 1 increase 5 times 5 G 1 0.8 as much!
Why the multiplier is greater than 1 Initially, the increase in G causes an equal increase in Y: Y = G. But Y C further Y further C further Y So the final impact on income is much bigger than the initial G.
SAMPLE QUESTIONKeynesian equilbrium: Solution procedureStart with the equation in general form:Y = a ( Y - T) + Ip + G + NXSubstitute in the given numbers:Y = 0.8 ( Y - 1000) + 1500 + 1200 + 500Collect all the constant terms:Y = 3200 + 0.8Y - 800Y = 2400 + 0.8YSubtract 0.8 Y from both sides of the equation:0.2 Y = 2400Finally, multiply both sides by 1 / 0.2 = 5Y = 5 (2400) = 12,000
SAMPLE QUESTIONThe MultiplierRerun the previous exercise, raising planned investment by 500.Y = 0.8 ( Y - 1000) + 2000 + 1200 + 500Collect all the constant terms:Y = 3700 + 0.8Y - 800Y = 2900 + 0.8YSubtract 0.8 Y from both sides of the equation:0.2 Y = 2900Finally, multiply both sides by 1 / 0.2 = 5Y = 5 (2900) = 14, 500GDP is UP BY 2,500, NOT up by only 500.Investment spending has a MULTIPLIER EFFECT of 5
Balanced Budget Multiplier with Lump-Sum Taxes (Cont.)The balanced budget multiplier: Y Y =1/(1-c) - c/(1- c) = 1 G T A change of 100 in both G and T also raised income by 100. Balanced change in G and T is not macro economically neutral. Balanced budget multiplier holds that if government revenues and expenditure increase or decrease simultaneously and equally, then national income will also change in the same amount - which means that the balanced budget multiplier equals to 1.
Unemployment rate: ◦ the percentage of the labour force without a job but registered as being willing and available for work Labour force ◦ those people holding a job or registered as being willing and available for work Participation rate ◦ the percentage of the population of working age declaring themselves to be in the labour force 27 .1 2
Measuring Unemployment• A Working Definition of Unemployment – People able, available and willing to find work and actively seeking work – but not employed – The unemployed are included in the labour force
Frictional Unemployment: Frictional unemployment is a temporarycondition. This unemployment occurs when an individual is out of hiscurrent job and looking for another job. The time period of shifting betweentwo jobs is known as frictional unemployment. The probability of getting ajob is high in a developed economy and this lowers the probability offrictional unemployment. There are employment insurance programs to tideover frictional unemploymentStructural Unemployment: Structural unemployment occurs due to thestructural changes within an economy. This type of unemployment occurswhen there is a mismatch of skilled workers in the labor market. Some ofthe causes of the structural unemployment are geographical immobility(difficulty in moving to a new work location), occupational immobility(difficulty in learning a new skill) and technological change (introduction ofnew techniques and technologies that need less labor force). Structuralunemployment depends on the growth rate of an economy and also on thestructure of an industry.
Types of unemploymentClassical Unemployment: Classical unemployment is also known as thereal wage unemployment or disequilibrium unemployment. This type ofunemployment occurs when trade unions and labor organization bargainfor higher wages, which leads to fall in the demand for labor.Cyclical Unemployment: Cyclic unemployment when there is a recession.When there is a downturn in an economy, the aggregate demand for goodsand services decreases and demand for labor decreases. At the time ofrecession, unskilled and surplus labors become unemployed. Read aboutcauses of economic recession.Seasonal Unemployment: A type of unemployment that occurs due to theseasonal nature of the job is known as seasonal unemployment. Theindustries that are affected by seasonal unemployment are hospitality andtourism industries and also the fruit picking and catering industries.
New hires Recalls Working Unemployed Job-losers Lay-offs Quits Retiring Discouraged Temporarily workers leaving Out of the Re-entrantsTaking labour force New entrants a job 27 .1 6