Question

Graphically derive the saving function if the consumption function is:

C+ a + bY

Note: In your Graph indicate and explain the following positions: Y>C;

Y<C; Y=C

Answer 1

$$solution$$

$Saving \ function\ can\ be\ derived from\ the\ consumption\ function\ as\ follows;\\$

$S=f(Y)\\ Y=C+S\\ S=Y-C$

$thus\ savings\ is \ the\ amount \ of income\ not \ spent\ in \ consumption;\\$

$therefore;\\ C=C-cY\\ S=Y-C-cY\\ S=-C+Y(1-c)\\$

$C \ is \ MPC$

$As \ change\ in\ income\ is \ devoted \ either \ to \ a \ change\ in \ consumption\\ or \ a\ change\ in \ saving\ or\ to\ both, \ therefore,\ the \ two \ ratios, \ that\ is;$

$[\frac{∆C}{∆Y }]\ and\ [\frac{ ∆S}{∆Y}]\ should \ add\ up\ to\ 1.\\ MPC + MPS = 1\\ or \ 1 – MPC = MPS \ or\ (1 – c) \ is \ the \ MPS$

$Where\ MPC\ represents\ the \ slope \ of\ consumption \ curve \ and \ MPS\ (1 – c)\\ represents \ the\ slope \ of\ saving \ curve.\\ As\ MPS\ is\ positive, \ therefore, \ saving\ is \ an\ increasing \ function\ of\ the\\ income\ level,\ i.e.,\ saving \ increases\ with\ increase\ in\ income.$

$for \ example$

$given;$

$As \ consumption\ is\ directly\ related\ to \ the \ income\ level, \ therefore\\ consumption \ curve\ is\ positively\ sloped. \\C = f(Y)$

$AD \ curve (C +I) \ is\ positively \ sloped.\ The gap \ between\ the\ consumption \\curve\ and\ AD \ curve\ is\ constant, \ that\ is,\ the\ two \ curves\ are\ parallel \\because\ Investment\ is \ constant.$

$Saving \ curve\ is \ positively\ sloped \ because\ saving\ is\ directly\ related\\ to\ the\ income\ level. S = f(Y)$

$At\ very \ low\ income\ level\ there\ is\ dissaving. Dissaving\ implies \ that\\ consumption\ is \ greater\ than\ the\ income\ level.\ This\ increased\ consumption\\ is\ met\ from\ past \ savings, \ therefore\ , there\ will \ be\ dissaving \\in\ the\ economy, e.g.\\ Y = 10\\ C = 15\\ Y = C + S\\$

$S = 10- 15\\ Or, S = -5\ → Dissaving$