If, in an economy, the minimum level of consumption is 45 and 80% of an increase in income(Y) is consumed, what will be the consumption function of this economy?

Let's break this down so it's crystal clear!

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We need to find the consumption function for this economy. The consumption function formula is:

$C = a + bY$

Where:

$C$ = Total consumption

$a$ = Minimum consumption (amount consumed even with zero income)

$b$ = MPC (Marginal Propensity to Consume)

$Y$ = Income

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From the question:

Minimum consumption $= 45$ → This is our $a$

$80\%$ of increase in income is consumed → MPC $= 80\% = 0.80$ → This is our $b$

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Plugging these values into the formula:

$C = 45 + 0.80Y$

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Why $0.80$ and not $80$?

When we say "$80\%$ of income," we write it as $0.80$ in the formula, NOT $80$

$80\% = \dfrac{80}{100} = 0.80$

If we wrote $80Y$, that would mean people consume $80$ times their income (MPC $= 80$), which is impossible since MPC cannot exceed $1$!

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Quick check of wrong options:

If you see $80Y$ → Wrong! MPC can't be more than $1$

If you see $20Y$ or $0.20Y$ → Wrong! That's only $20\%$, not $80\%$

$45 + 0.80Y$ → Correct! Minimum consumption of $45$, plus $80\%$ of income consumed

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Answer: $45 + 0.80Y$