The Slutsky Equation
The total effect of a price increase can thus be divided into a substitution and an income effect. In terms of the own price elasticity we can define the total effect as:
ΔQtot = ε . (Q0/p0) . Δp
the substitution effect is:
ΔQsub = ε∗ . (Q0/p0) . Δp
and the income effect:
ΔQinc = η . (Q0/Y0) . ΔY
In general we can write:
ΔQtot = ΔQsub + ΔQinc
ε . (Q0/p0) . Δp = ε∗ . (Q0/p0) . Δp + η . (Q0/Y0) . ΔY
If we use the Slutsky compensation criterion, that the consumer should be able to buy her initial bundle of consumption goods, x0, the income compensation can be written as:
ΔY = Δp . Q0,
and we can rewrite the previous equation as,
ε .(Q0/p0) . Δp = ε∗ . (Q0/p0) . Δp + η (Q0/Y0) . Δp . Q0,
we now multiply and divided the last term on the right-hand side by p0 and after that we cancel all common terms:
ε . (Q0/p0) . Δp = ε∗ . (Q0/p0) . Δp + η . (Q0/Y0) . (p0/p0) . Δp . Q0,
ε = ε∗ + η . [(Q0 . p0)/Y0]
The very last term now shows the budget share of the good whose price has changed, or
θ = (Q0 . p0)/Y0
Note that Q0.p0 gives the total expenditure on that particular good and Y0 is total expenditure on all good, given that the consumer uses all her budget to buy goods. Hence, we can finally write the Slutsky equation in terms of elasticity,
ε = ε∗ + η . θ
We should now remind ourselves that for a price increase the total effect is negative if the good is a normal good; the substitution effect is always negative (so the compensated price elasticity ε∗ is always negative). The income effect is positive for a normal good, but in the case of a price increase the consumer’s real income decreases so the second term on the right-hand side is also negative (η < 0). If the good in question is an inferior good, the income effect is negative which means that demand for the good increases as the real income decreases and η > 0. In this case the sign of the total effect is unclear. This means that the uncompensated demand curve could be upward sloping (for a very inferior good). Such goods are called Giffin goods and could be a reality especially in poor countries their families are very dependent on a particular source of food for their survival (e.g. potatoes or maize). But, Gi?en goods must be considered to very unusual cases which goes against the “law of demand” (i.e., that the demand curves are downward sloping).
One more comment on the Slutsky equation is in order. In the derivation we assumed Slutsky compensation criterion instead of Hicks’. This was done to make the derivation easier, but it can be shown that for small price changes, the two compensation criteria coincide and we get the same final expression.
Latest technology based Economics Online Tutoring Assistance
Tutors, at the www.tutorsglobe.com, take pledge to provide full satisfaction and assurance in Intermediate Microeconomics homework help via online tutoring. Students are getting 100% satisfaction by online tutors across the globe. Here you can get homework help for Intermediate Microeconomics, project ideas and tutorials. We provide email based Intermediate Microeconomics homework help. You can join us to ask queries 24x7 with live, experienced and qualified online tutors specialized in Intermediate Microeconomics. Through Online Tutoring, you would be able to complete your homework or assignments at your home. Tutors at the TutorsGlobe are committed to provide the best quality online tutoring assistance for Economics homework help and assignment help services. They use their experience, as they have solved thousands of the Computer assignments, which may help you to solve your complex issues of Intermediate Microeconomics. TutorsGlobe assure for the best quality compliance to your homework. Compromise with quality is not in our dictionary. If we feel that we are not able to provide the homework help as per the deadline or given instruction by the student, we refund the money of the student without any delay.
tutorsglobe.com secondary treatment assignment help-homework help by online sewage treatment and disposal tutors
Plant-Water Relations tutorial all along with the key concepts of Cellular water relations, Stomatal mechanism, Transpiration process and Water translocation
Hardey-Weinberg Principle tutorial all along with the key concepts of Modern theories of Evolution, Illustrations of the Hardy-Weinberg Principle, Derivation of the Hardy-Weinberg Principle, Implications of the Hardy-Weinberg Law
theory of wall-hugging robot all along with the key concepts of the wall-hugging robot, finite state machines. tutorsglobe offers homework help, assignment help and tutor’s assistance on tutorsglobe offers homework help, assignment help and tutor’s assistance on the wall-hugging robot.
www.tutorsglobe.com offers parabola homework help, parabola assignment help, online tutoring assistance, general form of parabolas, standard form of parabolas math solutions by online qualified geometry mathematics tutor's help.
Theory and lecture notes of Turing machines and the automata of equal power all along with the key concepts of turing machines and the automata of equal power, Finite Automata with External Storage, queue automaton. Tutorsglobe offers homework help, assignment help and tutor’s assistance on Turing machines and the automata of equal power.
Vegetative Structure of Seed Plants-Root tutorial all along with the key concepts of Root Growth, Types of roots, Taproot system, Fibrous root system, Specialized Variations of Roots and Root architecture
tutorsglobe.com energy resources assignment help-homework help by online natural resources tutors
Systematic Classification of Algae tutorial all along with the key concepts of Rhodophycophyta, Xanthophycophyta, Chrysophycophyta, Phaeoophycophyta, Bacillariophycophyta, Euglenophycophyta, Chlorophycophyta, Cryptophycophyta and Pyrrophycophyta
Put a full stop to all your academic struggles by acquiring European History after 1715 Assignment Help from PhD tutors.
tutorsglobe.com php assignment help-homework help by online computer programming tutors
tutorsglobe.com selling costs assignment help-homework help by online characteristics of monopolistic competition tutors
Mechanism of Genetic Variation and Hereditary tutorial all along with the key concepts of Genetic Variation, Mutation, Spontaneous Mutation, Induced Mutation, Types of Mutation, Genetic Recombination and Mechanism of Recombination
tutorsglobe.com laboratory diagnosis and control assignment help-homework help by online clostridium botulinum tutors
Fats and Oil tutorial all along with the key concepts of Occurrence and Composition of Fats, Formation of Fats and Oils, Structure of Fats and Oils, Properties of Fats and Oils, Analysis of Fats and Oils, Uses of Fats and Oil and Soaps
1941436
Questions Asked
3689
Tutors
1456205
Questions Answered
Start Excelling in your courses, Ask an Expert and get answers for your homework and assignments!!