Pbar is the end of the curve closest to the right the

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(Pbar is the end of the curve, closest to the right) The transformation curve Trade off b/t crime in the rich/poor neighborhoods Pr+Pp = P(bar) Cp decreases, Pp increases Pr decreases, Cr increases See figure 10.9 transformation curve Backwards J curve All in poor is at the top end , all in rich is at the bottom end
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Midpoint is Pr=Pp, =P(bar)/2 → Cp>Cr if moving all police from midpoint A to midpoint B P(bar)/2 → Cp<Cr if moving from All in poor to all in rich A = (midpoint b/t all P in poor and midpoint and B = (midpoint b/t midpoint and all P in rich) Equal number of police means more crime in poor neighborhood Vertical arrow downward is greater than horizontal arrow to the right for the curve because the additional policeman is more productive in the rich neighborhood than the poor one. How to choose police allocation See figure 10.10 allocating the police Use 45 degree angle to cut the curve (Cr=Cp, Pp>Pr), (Pbar/2 - Cp>Cr) 1. Equal opportunity: protection against crime is equal 2. Equal outcomes: crime is the same in both neighborhoods 3. Minimize total crime: iso-crime lines a. Total crime is constant i. Cr + Cp = k ii. dCr/dCp = -1(slope of iso-crime line) 1. This intersects negatively and tangentially a. Cr<Cp → Pr>Pp 4. Minimize weighted crime a. Cr + 2Cp = k i. Cr is weighted iso-crime line ii. Slope is -2 (steeper than iso-crime line) Summary Individuals choose b/t criminal activity and legitimate employment to secure best income The disadvantaged tend towards crime # criminals increases as disadvantaged population rises Falls w/increase in crime-prevention spending(reduce criminal income) Congestion effects added to both criminal/police sides, multiple equilibria occurs Imitation behavior (one criminal mimics crime of others) produces big swings inc rime across neighborhoods Society’s objectives determines allocation of police to reduce crime in rich/poor neighborhoods Chapter 11 Urban quality-of-life measurement Amenity Prominent role in real estate markets west/east coast locations superior to interior bc of better weather and ocean access Housing prices (factor for amenity compensation) Provide compensating differential Lower housing price bc ‘disadvantage’ of amenity
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Higher housing price bc more desirable living region + amenities Interregional comparisons Income differences (another factor for amenity) Increasing compensating differential One economic agent → firms → pay incomes → real estate → prices Roback model (theory) 2 underlying equilibrium conditions -consumers are at a common level of utility (u bar) -firms are at a common level of zero-profits ( 𝝅 bar) = 0 Consumer analysis: -bread, housing, amenities -u(c,q,a) 1. Amenities are a bundle A: (weighted) index, or vector Define each amenity in a positive manner a 0 (high crime) a 1 (low crime) V: indirect utility function v(y,p,a) y=income p=price per sq. ft of real estate/housing a=amenity level dv/dy>0 dv/dp<0 dv/da>0 v(y,p,a) = v(bar) Combos of y and p that result in the same level of utility See figure 11.1 indifference curves
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