3.7
The savings function illustrates how much people save at different levels of disposable income.
Economists express savings as the difference between disposable income and consumption, which can be represented using the formula S = Yd - C. By substituting the consumption function into this formula, we get a new equation.
In this equation, “–a” is the intercept, which shows savings when disposable income is zero. This value is usually negative, indicating borrowing.
The term “(1 – b),” or the marginal propensity to save, is the slope. It shows the change in savings for each additional unit of disposable income.
Consider a = 200 and b = 0.75. Then, the savings function becomes as shown. At a disposable income of 100, savings S = –175. This negative value indicates that people are still dissaving—spending more than they earn.
However, at a disposable income of 1000, savings S = 50. This positive value means households are now saving—setting aside part of their income.
De spaarfunctie verklaart hoe individuen een deel van hun inkomen sparen nadat zij in hun consumptiebehoeften hebben voorzien. Zij legt een wiskundige relatie vast tussen inkomen (Y), consumptie (C) en sparen (S):
S = Y − C
Waarbij:
Deze identiteit maakt duidelijk dat sparen het deel van het inkomen vormt dat niet aan consumptie wordt besteed.
De consumptiefunctie
Consumptie wordt veelal weergegeven in lineaire vorm:
C = a + bY
Waarbij:
Afleiding van de spaarfunctie
Door de consumptiefunctie te substitueren in de spaarfunctie ontstaat:
S = Y − (a + bY)
S = −a + (1 − b)Y
Dit is de spaarfunctie, waarbij:
Numeriek voorbeeld
Stel: a = 200 en b = 0,75.
Dan luidt de spaarfunctie:
S = −200 + 0,25Y
Situatie 1: bij inkomen (Y) = 100
S = −200 + 0,25 × 100
S = −175
Bij dit inkomensniveau is het spaarsaldo negatief. Dit duidt op ontsparen: het individu besteedt meer dan het verdient en doet dat waarschijnlijk door te lenen of het bestaande spaargeld te gebruiken.
Situatie 2: bij inkomen (Y) = 1.000
S = −200 + 0,25 × 1.000
S = 50
Hier is het spaarsaldo positief, wat betekent dat na consumptie een deel van het inkomen kan worden gereserveerd.
Grafische interpretatie
De spaarfunctie is een rechte lijn met:
De grafiek laat zien:
Belang van de spaarfunctie
De spaarfunctie heeft zowel micro- als macro-economische betekenis:
The savings function illustrates how much people save at different levels of disposable income.
Economists express savings as the difference between disposable income and consumption, which can be represented using the formula S = Yd - C. By substituting the consumption function into this formula, we get a new equation.
In this equation, “–a” is the intercept, which shows savings when disposable income is zero. This value is usually negative, indicating borrowing.
The term “(1 – b),” or the marginal propensity to save, is the slope. It shows the change in savings for each additional unit of disposable income.
Consider a = 200 and b = 0.75. Then, the savings function becomes as shown. At a disposable income of 100, savings S = –175. This negative value indicates that people are still dissaving—spending more than they earn.
However, at a disposable income of 1000, savings S = 50. This positive value means households are now saving—setting aside part of their income.
From Chapter 3:
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