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The relationship between the Marginal Propensity to Consume (MPC) and the Multiplier (K)



The Multiplier (K) is the ratio of a change in National Income to the change in government spending that cause it. The mechanism that gives rise to a multiplier effect is that an initial incremental amount of spending can lead to increased in consumption spending, increasing income further and hence further increasing consumption and whiles The Marginal Propensity to Consume (MPC) is defined as the proportion of the aggregate raise in pay that is utilized on the consumption of goods and services opposing to the amount being saved. It can also be defined as Induced Consumption as this shows the consumption of goods and services due to increase in disposable incomes.
The relationship between the Multiplier (K) and Marginal Propensity to Consume (MPC) is that, the multiplier relies on the MPC (Marginal Propensity to Consume) in an open economy. So, if there is an increase in the MPC it will eventually be an increase in the Multiplier and vice verse.
Some consumption maybe seen as more benevolent (to the economy) than others, Therefore, spending could be targeted where it would do most benefit, thus generate the highest (close to 1) MPC.
Let assume consumption increases by eighty percent (80%) for each additional Ghana Cedi’s (GH₵) of income of a worker in Ghana. By which:
         
         MPC =        Change in Consumption (∆C)    
Change in Income (∆Y)
            =       0.8           = 0.8
                                  1

Suppose rLg Communication, an IT firm in Ghana partnering Microsoft Corporation and South Africa’s GUMA Group of Companies to build HOPE City project at Donkonaa, an area between Weija and Kasoa. To spend on the project for the first year is GH₵ 5 Billion which is to go to electricians, engineers and others. If the MPC is equal to 0.8, those people will spend GH₵ 4 Billion.
Mathematically;
        
           MPC =       Change in Consumption (∆C)     
Change in Income (∆Y)
                     =        GH₵ 4 Billion              =   0.8
                              GH₵ 5 Billion
              Then, Multiplier (k) =             1          
                                                      1 - MPC
            =         1
               1 – 0.8
         =         1         = 5
                  0.2

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