Question

Consider a firm with supply curve given by q(p) = p^1/2 If the firm faces a...

Consider a firm with supply curve given by q(p) = p^1/2

If the firm faces a price decrease from $25 to $16, what fraction of the total reduction in producer surplus is attributed to "units leaving the market"?

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Answer #1

Supply :

q = p1/2

When price = 25

q = 251/2 = 5

when price = $16

q = 161/2 = 4

Producer surplus before price reduction = ( 1/2)* 25*5 = $62.5

Producer surplus after price reduction = (1/2)*16*4 = $32

Total reduction = 62.5 - 32 = 30.5

reduction in producer surplus is attributed to units leaving the market = (1/2)*25*(5-4)

= $12.5

fraction of the total reduction in producer surplus is attributed to "units leaving the market"

= 12.5/30.5

= 25/61

= 0.4098

= 0.41

= 41%

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