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# aps3 - Intermediate Microeconomics Wissink BRIEF ANSWERS TO...

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- 1 - Intermediate Microeconomics - Wissink BRIEF ANSWERS TO PROBLEM SET #3 1. u(x,y) = y + B ln(x) x D = Bp y / p x and y D = I/p y - B η D x,px = |(dx D /dp x )| (p x / x) dx D / dp x = - B p y / p x 2 η D x,px = (B p y / p x 2 ) (p x / (Bp y /p x ) ) η D x,px = 1 always η D x,py = (dx D /dp y )(p y / x) dx D / dp y = B / p x η D x,py = (B / p x ) (p y / (Bp y /p x ) ) η D x,py = 1 always η D x,I = (dx D /dI) (I / x) dx D /dI = 0 η D x,I = 0 always 2. If X D = 100 – 2p η D x,px = 2 (p/X) = 2p / (100 – 2p) = p / (50 – p) if p=5 then η D x,px = .11 3. If u(x,y) = xy then x D = I/2p x and y D = I/2p y η D x,px = (I/2p x 2 ) (p x / (I/2p x )) =1 η D y,py = (I/2p y 2 ) (p y / (I/2p y )) =1 4. a.b. see diagram p 100 S 33.33 D R D W total D 33.33 50 66.67 100 150 X c. Market X D = 150 – (3/2) p and X S = 3p or p D = 100 – (2/3) X and p S = (1/3) X d. X D = X S 150 – (3/2) p* = 3p* p* = 33.33 and so X* = 100 Workers: X D,W = 100 – p X* ,W = 66.67 Retired: X D,R = 50 – (12) p X* ,R = 33.33 e. At p=0 the demand from retired people is 50 X D = 150 – p if p 100 and X D = 50 if p >100 Need X D = X S 150 – p* = 3p* p* = 37.50 and X* = 112.50 X* ,W = 62.5 and X* ,R = 50 f. If I work and use the trolley I am not happy. The equilibrium price and quantity increase, the trolleys are more crowded and crowded with retired people. I pay more and less workers ride in the

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aps3 - Intermediate Microeconomics Wissink BRIEF ANSWERS TO...

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