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1660:
22:
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1297:
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Note that the utility function shows the utility for whatever quantities its arguments hold, even if they are not optimal for the consumer and do not solve his utility maximization problem. The indirect utility function, in contrast, assumes that the consumer has derived his demand functions
830:
1207:
1655:{\displaystyle v(p_{1},p_{2},w)=u(x_{1}^{*},x_{2}^{*})=(x_{1}^{*})^{0.6}(x_{2}^{*})^{0.4}=\left({\frac {0.6w}{p_{1}}}\right)^{0.6}\left({\frac {0.4w}{p_{2}}}\right)^{0.4}=(0.6^{0.6}*.4^{.4})w^{0.6+0.4}p_{1}^{-0.6}p_{2}^{-0.4}=Kp_{1}^{-0.6}p_{2}^{-0.4}w,}
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624:
1034:
1044:
488:
with degree zero in prices and income; if prices and income are all multiplied by a given constant the same bundle of consumption represents a maximum, so optimal utility does not change;
1720:
941:
449:
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This function is called indirect because consumers usually think about their preferences in terms of what they consume rather than prices. A consumer's indirect utility
378:
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243:
158:
275:
1232:
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1951:
825:{\displaystyle -{\frac {\partial v(p^{0},w^{0})/(\partial p_{i})}{\partial v(p^{0},w^{0})/\partial w}}=x_{i}(p^{0},w^{0}),\quad i=1,\dots ,n.}
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1202:{\displaystyle x_{1}(p_{1},p_{2})={\frac {0.6w}{p_{1}}}\;\;\;\;{\rm {and}}\;\;\;x_{2}(p_{1},p_{2})={\frac {0.4w}{p_{2}}},}
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333:
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of quantities of consumable goods, by first computing the most preferred affordable bundle, represented by the vector
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2183:
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1814:
Cornes, Richard (1992). "Individual
Consumer Behavior: Direct and Indirect Utility Functions".
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is found by replacing the quantities in the utility function with the demand functions thus:
507:
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380:
the consumer derives from that bundle. The resulting indirect utility function is
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2379:
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21:
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119:
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207:. It reflects both the consumer's preferences and market conditions.
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1933:
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when the prices are kept constant. I.e, for every price vector
15:
951:
Let's say the utility function is the Cobb-Douglas function
1915:(Second ed.). Hinsdale: Dryden Press. pp. 57–59.
619:{\displaystyle {\frac {\partial v(p,w)}{\partial w}}\neq 0}
1844:(Third ed.). Harlow: Prentice Hall. pp. 28–33.
1818:. New York: Cambridge University Press. pp. 31–62.
1234:
is the consumer's income. The indirect utility function
1029:{\displaystyle u(x_{1},x_{2})=x_{1}^{0.6}x_{2}^{0.4},}
1913:
Microeconomic Theory: Basic
Principles and Extensions
1896:. New York: Oxford University Press. pp. 56–57.
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840:
The indirect utility function is the inverse of the
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1967:
46:. Unsourced material may be challenged and removed.
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245:can be computed from his or her utility function
1036:which has the Marshallian demand functions
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1866:. New York: McGraw-Hill. pp. 103–107.
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106:Learn how and when to remove this message
1715:{\displaystyle K=(0.6^{0.6}*0.4^{0.4}).}
160:gives the consumer's maximal attainable
1798:(3rd ed.). New York: W. W. Norton.
1754:
1723:optimally for given prices and income.
7:
1800:, pp. 111, has the general formula.
1769:(Third ed.). New York: Norton.
336:, and second, computing the utility
44:adding citations to reliable sources
936:{\displaystyle v(p,e(p,u))\equiv u}
2508:Microfoundations of macroeconomics
1124:
1121:
1118:
743:
703:
685:
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454:The indirect utility function is:
14:
444:{\displaystyle v(p,w)=u(x(p,w)).}
184:of goods prices and an amount of
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2580:
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1282:{\displaystyle v(p_{1},p_{2},w)}
836:Indirect utility and expenditure
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31:needs additional citations for
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482:Strictly increasing in income;
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1842:Advanced Microeconomic Theory
561:{\displaystyle (p^{0},w^{0})}
1816:Duality and Modern Economics
334:utility maximization problem
2453:Civil engineering economics
2438:Statistical decision theory
2078:Income elasticity of demand
55:"Indirect utility function"
2623:
2088:Price elasticity of supply
2083:Price elasticity of demand
2073:Cross elasticity of demand
1911:Nicholson, Walter (1978).
2564:
373:{\displaystyle u(x(p,w))}
164:when faced with a vector
124:indirect utility function
2144:Income–consumption curve
1738:Hicksian demand function
2478:Industrial organization
522:) is differentiable at
476:is the number of goods;
2607:Utility function types
1794:Microeconomic Analysis
1767:Microeconomic Analysis
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325:{\displaystyle x(p,w)}
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238:{\displaystyle v(p,w)}
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153:{\displaystyle v(p,w)}
2448:Engineering economics
2043:Cost–benefit analysis
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479:Decreasing in prices;
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277:defined over vectors
272:
270:{\displaystyle u(x),}
240:
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2265:Price discrimination
2159:Intertemporal choice
1894:Microeconomic Theory
1886:Whinston, Michael D.
1864:Microeconomic Theory
1860:Luenberger, David G.
1671:
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842:expenditure function
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40:improve this article
2576:Business portal
2513:Operations research
2340:Substitution effect
1790:Varian, H. (1992).
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2154:Indifference curve
2122:Goods and services
2063:Economies of scope
2058:Economies of scale
1882:Mas-Colell, Andreu
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864:and utility level
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2556:Political economy
2355:Supply and demand
2235:Pareto efficiency
1851:978-0-273-73191-7
1733:Gorman polar form
1508:
1471:
1227:{\displaystyle w}
1194:
1110:
877:{\displaystyle u}
857:{\displaystyle p}
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290:{\displaystyle x}
200:{\displaystyle w}
177:{\displaystyle p}
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2316:Returns to scale
2174:Market structure
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2048:Deadweight loss
1985:Consumer choice
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1890:Green, Jerry R.
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1808:Further reading
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510:states that if
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332:by solving the
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122:, a consumer's
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2551:Macroeconomics
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2250:Price controls
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2169:Market failure
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1961:Microeconomics
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1743:Value function
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508:Roy's identity
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458:Continuous on
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19:
13:
10:
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4:
3:
2:
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2483:Institutional
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2428:Computational
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2373:Law of supply
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2364:Law of demand
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2353:
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2350:Social choice
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2335:Excess supply
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2255:Price ceiling
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2110:
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2024:
2020:
2017:
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1995:
1994:non-convexity
1991:
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1978:
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1962:
1955:
1950:
1948:
1943:
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1932:
1924:
1922:0-03-020831-9
1918:
1914:
1909:
1905:
1903:0-19-507340-1
1899:
1895:
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1879:
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1873:0-07-049313-8
1869:
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1831:
1827:
1825:0-521-33601-5
1821:
1817:
1812:
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1807:
1796:
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1786:
1783:
1778:
1776:0-393-95735-7
1772:
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57: –
56:
52:
51:Find sources:
45:
41:
35:
34:
29:This article
27:
23:
18:
17:
2518:Optimization
2503:Mathematical
2463:Experimental
2458:Evolutionary
2443:Econometrics
2301:Public goods
2275:Price system
2270:Price signal
2184:Monopolistic
2053:Distribution
1968:Major topics
1912:
1893:
1863:
1841:
1834:Jehle, G. A.
1815:
1793:
1785:
1766:
1757:
1666:
1213:
950:
839:
519:
515:
511:
505:
499:
495:
492:quasi-convex
473:
466:
459:
453:
209:
123:
117:
102:
93:
83:
76:
69:
62:
50:
38:Please help
33:verification
30:
2468:Game theory
2433:Development
2380:Uncertainty
2260:Price floor
2240:Preferences
2179:Competition
2149:Information
2112:Externality
2095:Equilibrium
2036:Transaction
2014:Opportunity
1975:Aggregation
1838:Reny, P. J.
1763:Varian, Hal
2498:Managerial
2418:Behavioral
2291:Production
2228:Oligopsony
2068:Elasticity
1980:Budget set
1749:References
506:Moreover,
486:Homogenous
66:newspapers
2539:Economics
2411:Subfields
2306:Rationing
2223:Oligopoly
2218:Monopsony
2206:Bilateral
2139:Household
1990:Convexity
1694:∗
1639:−
1621:−
1597:−
1579:−
1537:∗
1429:∗
1401:∗
1377:∗
1359:∗
928:≡
811:…
744:∂
704:∂
686:∂
643:∂
637:−
611:≠
602:∂
579:∂
120:economics
2601:Category
2586:Category
2532:See also
2423:Business
2395:Marginal
2390:Expected
2331:Shortage
2326:Scarcity
2201:Monopoly
2107:Exchange
2019:Implicit
2009:Marginal
1892:(1995).
1862:(1995).
1840:(2011).
1765:(1992).
1727:See also
96:May 2021
2544:Applied
2523:Welfare
2385:Utility
2345:Surplus
2284:Pricing
2196:Duopoly
2189:Perfect
2132:Service
2100:General
2004:Average
947:Example
626:, then
162:utility
80:scholar
2369:Supply
2360:Demand
2296:Profit
2164:Market
2026:Social
1919:
1900:
1870:
1848:
1822:
1773:
1667:where
1214:where
472:where
186:income
82:
75:
68:
61:
53:
2488:Labor
2473:Green
2245:Price
2127:Goods
2117:Firms
87:JSTOR
73:books
2402:Wage
2311:Rent
2279:Free
2031:Sunk
1999:Cost
1992:and
1917:ISBN
1898:ISBN
1868:ISBN
1846:ISBN
1820:ISBN
1771:ISBN
568:and
494:in (
59:news
2493:Law
1702:0.4
1698:0.4
1689:0.6
1685:0.6
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118:In
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