Graphs In Thk Income Determination Model

2.7. Given: Y » C ♦ /. C -50+ 0-8K and ■ 50. (<r) Graph Ihc consumption function. (/») Graph the aggregate demand function. < 4 /». (c) Find the equilibrium level of income from the graph d) Since consumption is a function ol income. it is graphed on the sertieal axis; income is graphed «»n the horizontal See Rg, 2-7 When other cimiponents of aggregate demand such as Ci. and X / arc added to the model, they are also graphed on the sertieal aus It is easily determined from the linear form ol the consumption (unction that the vertical intercept is 50 and the slope of the line (Ihe MPC or ¿CA&WbOK.

h) Investment in the model is auumnnumx imannrnf This means investment is independent of incswnc and docs ih»i change in response to changes in income When omudcrcd by itself, ihe graph of a constant is a hmi/ontal line; when added to a linear function, it causes a parallel shift in the original function by an amount equal to it« value In fig. 2-7. autonomous investment causes the aggregate demand function to shift up by 50 parallel to the initial consumption function c) lb obtain the equilibrium level of income from a graph, a 45' dashed line is drawn from Ihc origin. II the «ame scale of measurement is used »hi both axes, a 45" line has a slope ol I. meaning tlut as the line moves away from the origin, it moves up vertically (AK) by one unit for every unit it moves across horizontally (A-V). Every pinnt on the 4V line, therefore, has a horizontal coordinate (<jhuttui)

Hg. 2.7

exactly equal to its vertical ciH.uJin.iic {ordinate). Consequently, when the aggregate demand function intersect» the 45' line, aggregate demand (a» graphed on the vertical) will equal national income (as graphed on ihe horizontal l Horn Fig. 2»7 it is clear thai the equilibrium lesel of income is 500. sincc the aggregate demand function (C *■ /) intersects the 45s line at 500.

2Jt. Given: >' - C" / > G. C»25 + 0-75K /-/«,« 50. and G » Ga « 25. <ti) Gtaph the aggregate demand function and show its individual compsincnK (/») Find Ihe equilibrium level of income, (r) How can the aggregate demand function be graphed directly, without having to graph each of the component parts?

c ) To graph ihe aggregate demand t unction directly, sum up the individual components

Ag* D C ♦ 1*0 25 + 0.75 V+ 50 ♦ 25 - 100 ♦ 0.75V

The direct graphing of the aggregate demand function coincide* exactly with the graph of the summation of the individual graphs of C. /. and <$ above

2.V. Use a graph to show how the addition of a lump-sum la* (a tax independent of in conic) influences the parameters of the income determination model Graph the two systems individually. using a solid line for (I) and a dashed line for (2).

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