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There are two goods in the economy - food F and light bulbs B (for the street light). Melody's utility is given by U =ln(F)+ ln (B) and her income is $80. Her neighbour's utility is given by U =2(F)^(1/2) + B^(1/2) and his income is $120. The prices are P(food) =2 and P(bulb)=1.
(a) How much of each good will she and her neighbour consume if neither attempts to free ride on each other's light? What is the total number of bulbs purchased between both? What are their actual utility levels?
(b) How much of each good will Melody purchase herself, if she attempts to free ride on her neighbour's light while her neighbour does no free riding? What is her utility level now?
(c) How much of each good will Melody and her neighbour purchase themselves, if both attempt to free ride on each other's light? What is the total number of bulbs purchased between both? What are their actual utility levels?
(d) Why does Melody manage to increase her utility from (a) to (b) even though the total quantity of bulbs is higher in (a)? Briefly explain. Which effect(s) is(are) responsible for Melody's quantity changes from (a) to (b) and (b) to (c)? Briefly explain.
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