Question

I 1. Suppose that Petra and Oliver must split 200 peanut bags between them. Petra's utility function is Up VCp and Oliver's utility function is Uo 1/2VCo where Cp and Co are the number of peanut bags Petra and Oliver consume, respectively (a) How much utility will Petra and Oliver receive if the peanut bags are split evenly between (b) If the social welfare function is W (c) If the social welfare function is W them? 1 mark between Petra and Oliver maximizes social welfare? 1 markl between Petra and Oliver maximizes social welfare 1 mark Up Uo,then what distribution of peanut bags min(Up, Uo), then what distribution of peanut bags

Answer 1

A)

If the split the peanut bags evenly, then each will get 100 bags.

  $U_{p} = \sqrt{C_{p}} \Rightarrow U_{p} = \sqrt{100}\Rightarrow U_{p} = 10$

A) If the split the peanut bags evenly, then each will get 100 bags u_p = squareroot C_p rightarrow u_p = squareroot u_p = 10 u_o = (1/2) squareroot C_0 rightarrow U_0 = (1/2) squareroot 100 rightarrow U_p = 5 B) W = U_p + U_o = squareroot c_p + (1/2) squareroot C_o This is a case of Benthamlte social welfare function, which measures social welfare as the total or sum of individual utility . This function will be maximized when bags are distributed evenly. Therefore, the distribution will be, Petra will get 100 bags and Oliver will also get 100 bags . W = min (C_P, C_o) It is called the Rawlsian social

$U_{o} = (1/2)\sqrt{C_{o}} \Rightarrow U_{o} =(1/2) \sqrt{100}\Rightarrow U_{p} = 5$

B)

$W = U_{p} + U_{o} = \sqrt{C_{p}} + (1/2)\sqrt{C_{o}}$

This is a case of  Benthamite social welfare function, which measures social welfare as the total or sum of individual utility.

This function will be maximized when bags are distributed evenly.

Therefore, the distribution will be, Petra will get 100 bags and Oliver will also get 100 bags.

C)

$W = min (C_{p},C_{o})$

It is called the Rawlsian social welfare function; it will satisfy the social welfare if we can find the find minimum value of utility by allocating given goods.

If we allocate all bags to Petra, he gets utility = $U_{p} = \sqrt{C_{p}} \Rightarrow U_{p} = \sqrt{200}\Rightarrow U_{p} = 10\sqrt{2}$

If we allocate all bag to Oliver, he gets utility = $U_{o} = (1/2)\sqrt{C_{o}} \Rightarrow U_{o} =(1/2) \sqrt{200}\Rightarrow U_{p} = 5\sqrt{2}$

So, here we allocate 200 bags to Oliver and None to Petra.