A

social welfare function

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is thought to be additive along the lines proposed by Bentham and$$ Mill:

Upper W equals Upper U $1$ plus Upper U $2$ plus $...$ plus Upper U Subscript nW$=$U$1+$U$2+...+$Un

where

Upper U Subscript iUi

is individual$$ i$\text{'}$s utility and there are n individuals.

Part $2$

Suppose an economy is made up of two$$ individuals, John and Jane. $$ John's utility function is

Upper U Subscript JohnUJohnequals$=49$ StartRoot Upper X EndRoot$49$X

and$$ Jane's utility function is

Upper U Subscript JaneUJaneequals$=33$X$.$

Part $3$

There is a fixed quantity of good X

$(4040$

$$units$)$ evenly divided between John and Jane

$(2020$

units for$$ each$).$

Part $4$

Social welfare$($W$)$ is equal$$ to:

Wequals$=$enter your response here

utils.$($Enter your response rounded to the nearest whole$$ number.$)$

Part $5$

Social welfare could be improved if a portion of good X were transferred from

$$

$$

John

Jane

to

$$

$$

Jane

John

$.$