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By directly non essential, I mean things like sports, research at public universities etc. How should a government decide how much of the yearly budget to keep for such things? Is there some way to figure out what is the right amount to invest in such fields?

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There isn't any right amount generally. The most efficient way to allocate government resources (regardless whether we are talking about things you consider essential or non-essential) is to allocate resources in a way that maximizes some social welfare function.

Social welfare function depends on what sort of goals/values government wants to pursue.

For example, social welfare function could be given by:

$$W(x_1,x_2)= x_1^ax_2^{1-a} \quad st \quad y=px_1 +qx_2$$

where $x_1$ would be essentials and $x_2$ non essentials, $y$ government budget and $p$ and $q$ price of essentials and non-essentials.

With government believing $a=1$ the most efficient thing would be to spend whole government budget only on essentials and completely ignore non-essentials (e.g. 0 money for sports, arts etc). If $a=0$ most efficient way would be to spend entirety of budget only on non-essentials. The most efficient allocation of budget to essentials or non-essentials will always be one that maximizes the welfare function and thus given by $\max W.$

However, different welfare functions (and the same welfare function with different parameters) will give you different amount of spending and there is no objective 'correct' welfare function, since what objectives government should pursue is matter of philosophy not science.

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  • $\begingroup$ How would one determine a precise value for "a"? $\endgroup$
    – Babu
    Nov 23, 2022 at 21:00
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    $\begingroup$ @TrystwithFreedom you can pick any value you want based on your ideology. Suppose you are essential 'fanatic' - then a is 1. Suppose you are non-essential fanatic then a=0. If you are neither essential fanatic nor non-essential fanatic a will be something in between 0 and 1. a is the intensity with which you believe government should prefer essentials to non-essentials. Any value is equally valid. You can use philosophy or religion to figure out what a should be, there is no objective answer $\endgroup$
    – 1muflon1
    Nov 23, 2022 at 21:03
  • $\begingroup$ Damnit, why does everything boil down to philosophy in the end :( $\endgroup$
    – Babu
    Nov 23, 2022 at 21:03
  • $\begingroup$ @TrystwithFreedom science is descriptive not prescriptive. $\endgroup$
    – 1muflon1
    Nov 23, 2022 at 21:04
  • $\begingroup$ @1muflon1 not economics though - economic science is often used to justify how governments "should" spend money or make laws. For example it's very important that house prices go up indefinitely, because economists say bad things will happen if they go down, therefore government prevents building of new houses. $\endgroup$ Nov 24, 2022 at 13:31

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