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7/25/2019 4. Consumer Optimum
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4. Consumer OptimumMax utility on budget set constrained optimization
Most preferred aordable consumption bundle
• Highest feasible utility
Economic Rationality
• Decision maker chooses most preferred alternative from availables
• Optimal choice: where indierence curve is tangent to budget line
• Choice set: available choiceso Most preferred bundle in choice set located
Rational constrained choice:
7/25/2019 4. Consumer Optimum
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• oundary optimum: where indierence curve isn’t tangent to budget
line & meets at the endo Consuming 0 units of good !not tangent to budget ling
• !nterior optimum: where indi"curve is tangent to budgetline in between
• More thank # tangency$ only above optimal
• Convex preference any point satis%es tangency conditionmust be an optimal point
• Strict convex only # optimal choice
Rational Constrained Choice: Ordinary "emands
• ordinary demand: Most preferred aordable bundle at given prices and budget
o denoted by
• contrast with compensated demand utility constant
Rational Constrained Choice
x#$ 0 and x%$ 0 interior !not boundary'
• if$
o buying !(#)*()' costs +m
budget is exhausted
7/25/2019 4. Consumer Optimum
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• when$
o (#) 0 and () 0 ,-./1-213
o !(#)*()' exhausts the budget
o indierence curves have 4no kinks’
ordinary demands obtained by solving$
a' p#x#$ & p%x%$ ' yb' slopes of budget constraint !5p#6p' and of indi"curve through
!(#)*()'are 7 at !(#)*()'
(x#$)x%$* satis%es conditions
a' budget is exhausted8p#(#) 9 p() 7 m
b' slope of budget constraint!5p#6p' and of indi"curve through !(#)*()'are 7 at !(#)*()'
Computing Ordinary "emands
info used to calculate !(#)*()' for given p#*p* and m:
Cobb5Douglas ;reference
MR+
<t !(#)*()'* M1= 7 5p#6p
(,*
!(#)*()' e(hausts the budget
(* p#(#) 9 p() 7 m
=ub !<' into !>' & simplify$ (#)
sub (#) in !>' & simplify$ ()
7/25/2019 4. Consumer Optimum
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cobb5Douglas used in e(amples$
o buying6selling
o intertemporal choice
o e(change e?uilibrium
Rational Constrained Choice
• if (#) 7 0 8 or () 7 0
o if either 7 0 ordinary demand is at a corner solution to the problem of
ma(imi@ing utility subAect to constraint
Corner =olution$ ;erfect =ub
B!(#*(' 7 (# 9 ( most preferred !(#)*()'
• 2ptimal choice usually on boundary
Example:
− 2ptimal bundle when p# 7 p:
o hen slope of straight indierence curve 7 slope of budget constraint'
Corner =olutions$ .on5Conve( ;references