Understanding the Slutsky Decomposition: Substitution & Income Effect

Transcription

1 Understanding the Slutsky Decomposition: Substitution & Income Effect age 1 lacement of the Final Bundle when p : Substitute or Complement Goods? egion A egion B egion C BC 2 S When p, BC rotates inwards becomes steeper Let the original bundle be ( p, y p ) The new budget constraint is divided into three regions, egion A, B and C These region are developed based on the location of the original bundle, bundle. The relation between the two goods, whether and y are substitutes or complements or is a giffen good depends on which region the final bundle falls on. So to find the relationship between the two goods, we compare the final bundle to the original bundle. If the final bundle falls in : egion A Say, at Bundle where: < y > y We see that as price of good increases, the individual buys less and more y i.e. he/she switches from a more epensive to a cheaper y so and y are SUBSTITU goods. Since quantity demanded of as p, is an THDX good egion B Say, at Bundle where: < y < y We see that as price of good increases, the individual buys less of both and y i.e. the goods are jointly consumed - CMLEMENTS Also, since quantity demanded of as p, is an THDX good egion C Say, at Bundle where: S > y S < y Since quantity demanded of as p, is an GIFFEN good

2 lacement of the Intermediate Bundle when p : Normal or Inferior Goods? age 2 M egion A egion A N egion B L egion C BC 3 BC 2 If the intermediate bundle falls in: To distinguish between the substitution and income effect, we draw the intermediate budget constraint, BC 2 BC 2 must have the same slope as the final Budget Constraint, BC 3 thus incorporating the new price ratio. However, BC 2 must go through the original bundle, this denotes that some income is given to the individual so that he can maintain the same purchasing power as before. Let the final bundle be (, y ) BC 2 id divided into three regions based on the location of the final bundle and the original bundle. Where the intermediate bundle lies, in comparison to the final bundle, indicates whether the goods are normal or inferior. So, to find out whether the good is normal or inferior we compare the intermediate bundle to the final bundle (Why?) Say, at Bundle M where: M < y M > y We see that as income is given to the individual falls and y rises i.e., as I, - so is an INFEI good as I, y - so y is a NMAL good egion B Say, at Bundle N where: N > y N > y We see that as income is given to the individual both and y rises. i.e., as I, - so is a NMAL good as I, y - so y is a NMAL good egion C Say, at Bundle L where: L > y L < y We see that as income is given to the individual rises but y falls. i.e., as I, - so is a NMAL good as I, y - so y is an INFEI good

3 Drawing the IC and BC to show the Slutsky Decomposition: Tips 1. First, draw the original BC and final BC and decide the location of the original and final bundle based on the relationship between the two good When the relationship between the two goods is not mentioned (choose the relationship which will make it easiest for you to draw in the ICs later on) 2. Then draw the intermediate BC and draw in the intermediate bundle based on whether good is normal, inferior or a giffen good. 3. Lastly draw in the ICs make sure they are always tangent to the BC at the original, intermediate and final bundle. Also, make sure your ICs do not intersect. age 3 So, what is the SLUTSKY DECMSITIN? Since Slutsky was the first economist to figure out that the total effect of a price change is caused by two separate effects : the substitution effect () and the income effect () the process of breaking the total effect () down into the and the is referred to as the Slutsky Decomposition. What will be the sign of the and? Sign of Sign of the is always negatives Why let s see When p, d of because compared to good y, good has become less attractive When p, d of because compared to good y, good has become more attractive Since there is always this inverse relationship between p and d of, the sign of the is ve. Sign of Sign of the may be positive or negative depends on whether the good is normal or inferior: If good is normal, i.e., wen I, - income and demand move in the same direction i.e. is +ve. If good is Inferior, i.e., wen I, - income and demand move in opposite directions i.e. is ve. Which effect is stronger? Normal Good and reinforce each other both work in the same direction Inferior Good and work in opposite directions Giffen Good outweighs this eplain how d of as p,

4 Slutsky Decomposition for a Normal Good when rice Increases age 4 The ed Dotted lines help to determine where the intermediate bundle should be Since is a Normal good, as income is given to individual, he should buy more of at than at Location of indicates that as p, individual buys less and more y than at i.e. the goods are Substitutes BC 3 BC 2 Step 1: Draw the BCs and bundles Step 2: Draw in the ICs Step 3: Mark the and Note: You may need to shift around your bundles a little so your ICs do not to cross! Note that the reinforces the both contribute to the reduction in consumption of when p Since at, when income is given to the person, more y is bought than at y is a Normal good as well

5 age 5 Slutsky Decomposition for an Inferior Good when rice Increases Drawing Tip: Note that to have more space to draw my ICs, I made my initial BC flatter than before and place more to the right The ed Dotted lines help to determine where the intermediate bundle should be Since is an Inferior good, as income is given to individual, he should buy less of than at Location of indicates that as p, individual buys less and more y than at i.e. the goods are Substitutes BC 3 BC 2 Note that the partially offsets the Since at, when income is given to the person, more y is bought than at y is a Normal good when p, less bought since less attractive than y thus the reduces consumption of when p, real income falls, and so more of is bought thus the increases amount of bought This eplains why the and work in opposite directions.

6 age 6 Slutsky Decomposition for a Giffen Good when rice Increases The ed Dotted lines help to determine where the intermediate bundle should be Since is an Inferior good, as income is given to individual, he should buy less of at than at Location of indicates that as p, individual buys more than at i.e. is a Giffen good. Note that the outweighs the Since at, when income is given to the person, more y is bought than at y is a Normal good when p, less bought since less attractive than y thus the reduces consumption of when p, real income falls, and so more of is bought thus the increases amount of bought Since the is stronger than the, d of as p.

7 age 7 Slutsky Decomposition for Normal Good when rice Decreases When p, BC rotates outwards from to BC 3 - to distinguish between the and we draw the intermediate BC at BC 2 -the BC that passes through the original bundle, Bundle in order to retain the same purchasing power as before, but has the slope of BC 3 in order to incorporate the new price ratio. The ed Dotted lines help to determine where the intermediate bundle should be Since is a Normal good, as income is taken away from the individual, he should buy less of at than at Location of indicates that as p, individual buys more and less y than at i.e. and y are Substitute goods BC 2 BC 3 Since at, when income is taken away from the person, more y is bought than at y is an Inferior good Note that the reinforces the when p, more bought since more attractive than y thus the increases consumption of when p, real income rises, and so more of is bought thus the increases amount of bought This eplains why the and work together to increase the quantity demanded of

8 Slutsky Decomposition for Inferior Good when rice Decreases age 8 Location of indicates that as p, individual buys more and y than at i.e. and y are Complements The ed Dotted lines help to determine where the intermediate bundle should be Since is an Inferior good, as income is taken away from the individual, he should buy more of at than at BC 2 BC 3 Since at, when income is taken away from the person, less y is bought than at y is an Normal good Note that the partially offsets the when p, more bought since more attractive than y thus the increases consumption of when p, real income rises, and so less of is bought thus the decreases amount of bought This eplains why the and work in opposite directions.

9 age 9 Slutsky Decomposition for Giffen Good when rice Decreases Location of indicates that as p, individual buys less than at i.e. is a Giffen good The ed Dotted lines help to determine where the intermediate bundle should be Since is an Inferior good, as income is taken away from the individual, he should buy more of at than at BC 3 BC 2 Note that the outweighs the Since at, when income is taken away from the person, less y is bought than at y is an Normal good when p, more bought since more attractive than y thus the increases consumption of when p, real income rises, and so less of is bought thus the decreases amount of bought Since the is stronger than the, consumption of falls as p.