Question

The multiplier in a country is equal to$5$, and households pay no taxes. At the current equilibrium real GDP of $\backslash (14$trillion, total real consumption spending by households is $\backslash )12$trillion. What is real autonomous consumption in this country?

Short answer

The autonomous consumption is$0.8$ trillion at equilibrium real GDP.

Step-by-step solution

Introduction

Given that a country's multiplier is five, and its current equilibrium real GDP is trillion.

If households spend trillions on real consumption, the real autonomous consumption is determined as follows:

Without taxes, the consumption function is,$\mathrm{C}=\mathrm{a}+\mathrm{bY}$

Where:

localid="1651569477300" $\mathrm{C}$is Consumption in actual terms

localid="1651569485468" $\mathrm{a}$is Autonomous Consumption

localid="1651569491480" $\mathrm{b}$is Marginal Propensity to Consume(MPC)

localid="1651569494190" $\mathrm{y}$is real equilibrium GDP

Calculation of MPC

The MPC must be obtained.

The following formula is used to compute it:

$\text{Multiplier}=\frac{1}{1-\mathrm{MPC}}$

$5=\frac{1}{1-\mathrm{MPC}}$

$1-\mathrm{MPC}=\frac{1}{5}$

$1-\mathrm{MPC}=0.2$

$\mathrm{MPC}=0.8$

Calculation of real GDP the autonomous consumption 

The autonomous consumption was then computed as follows:

Consumption function in the absence of taxation:

$\mathrm{C}=\mathrm{a}+\mathrm{bY}$

Here

localid="1651569839080" $\mathrm{c}$islocalid="1651569647212" $\$12\mathrm{trillion}$

localid="1651569657248" $\mathrm{b}$islocalid="1651569669645" $0.8\left(\mathrm{MPC}\right)$

localid="1651569675518" $\mathrm{y}$islocalid="1651569691437" $\$14\mathrm{trillion}$

localid="1651569719142" $12=\mathrm{a}+(0.8\times 14)$

localid="1651569726530" $\mathrm{a}=12-11.2$

$=0.8$