PS11+homework - the other allocations explain why it is not...

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Intermediate Microeconomics, 2010 Problem Set 11: Homework Due Wed/Thurs Feb. 17/18 1. Consider the following quasilinear economy: A rm can produce metal at costs c ( q s ) = 1 4 ( q s ) 2 . A consumer has preferences over metal and money: U m; q d = m + v q d = m + 10 q d 1 4 q d 2 : The initial income of the consumer is Y = 0 (Recall: Negative m is ok and will happen here.) For each of the following allocations [ q s ; q d ; ; m ] determine if the allocation is feasible and explain your reasoning (Hint: A good explanation for why an allocation is not feasible will cite which one of the conditions for feasibility is violated): (a) [ q s ; q d ; ; m ] = [5 ; 10 ; 25 ; 50] (b) [ q s ; q d ; ; m ] = [12 ; 10 ; 25 ; 50] (c) [ q s ; q d ; ; m ] = [12 ; 10 ; 25 ; 100] (d) [ q s ; q d ; ; m ] = [10 ; 10 ; 25 ; 50] 2. For the quasilinear economy in the previous problem, determine which of the following allocations is a competitive allocation at the price given.
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Unformatted text preview: the other allocations, explain why it is not a competitive allocation (Hint: Cite one of the conditions for a competitive allocation). (a) [ q s ;q d ;±;m ] = [5 ; 10 ; 25 ; ± 50], p ± = 10 (b) [ q s ;q d ;±;m ] = [10 ; 10 ; 25 ; ± 50], p ± = 5 (c) [ q s ;q d ;±;m ] = [10 ; 10 ; 25 ; ± 100], p ± = 10 (d) [ q s ;q d ;±;m ] = [10 ; 10 ; 25 ; ± 50], p ± = 5 3. Consider the following quasilinear economy: A ±rm has cost c ( q s ) = 8( q s ) 2 and a consumer gets utility from money and consuming the good according to U ( m;q d ) = m + ln( q d ). The initial income of the consumer is Y = 20. Find the competitive allocation [ q ± ;q ± ;± ± ;m ± ] and price, p ± for this economy. 1...
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