Lecture 5. How to find utility maximizing bundle/ optimal bundle. A consumer if better off if he can reach to a higher indifference curve. Due to the limited resource he has to be on the budget line.
So A is the optimal bundle that is the solution to the utility maximization
Case 1: If the price of one good is increased ( price of other good remains the same) then the budget line will rotate inward.
Example: Suppose the budget line is 2X+ 2Y= 400. So the price of X is Px=2. Now if the price of X increases to Px=4 then the budget line will rotate inward.
When there is an increase in income the budget line shifts to the right. So we can find the optimal bundle by shifting the indifference curve to the right and finding the tangency point. Usually in the new optimal bundle the amount of both of the goods will be increased. So the utility level will be increased as the consumer is consuming more of both of the goodswhen the income increases.
Example: In our example the budget line was 2X+ 2Y=400. So the income is 400. Now if the income increases to 800 then the budget line shifts to the right.
When there is an decrease in income the budget line shifts to the left. So we can find the optimal bundle by shifting the indifference curve to the left and finding the tangency point. Usually in the new optimal bundle the amount of both of the goods will be decreased. So the utility level will be decreased as the consumer is consuming less of both of the goods when the income decreases.
So we can write
Price Effect = Substitution Effect + Income Effect
Or, PE = SE + IE
Suppose, we have two goods: Fine rice and Coarse rice. We exhaust our budget by consuming this two goods. When the price of fine rice decreases there are two sorts of effects:
Substitution Effect: As the price of fine rice has increased so we will want to substitute fine rice with coarse rice. That means as fine rice becomes relatively expensive we will want to replace fine rice with coarse rice. So we will decrease fine rice consumption and increase coarse rice consumption. This decrease in fine rice consumption due to the increase in relative price of fine rice is known as substitution effect.
Income Effect: As the fine rice becomes expensive we can now buy less fine rice with the same level of income. That means our purchasing power has decreased. This decrease in consumption of fine rice due to decrease in purchasing power is known as income effect.
Here our budget line is 2X + 2Y= 400 and initially our optimal bundle is X=100 and Y=100. Now suppose the price of X ( Fine Rice) increases to 4 ( initially it was 2). So in the new optimal bundle we consume 60 fine rice. We know that the price effect is the change in consumption due to change in price. So here price effect PE= 60-100= -40.
Now we can break down this price effect into substitution effect and income effect.
Suppose we decrease our consumption of fine rice by 30 ( kg) because we substitute fine rice with coarse rice. So substitution effect , SE= -30.
And we decrease our consumption of fine rice by 10(kg) due to the decrease in purchasing power ( as price of fine rice is increased we cannot buy the same amount of fine rice). So income effect , IE=-10
Thus PE= SE+ IE
is the Slutsky equation
He will try to substitute fine rice with its alternative, like coarse rice. That is he will decrease fine rice consumption and increase coarse rice consumption. So we can write
Price of Fine Rice↑ => Quantity of Fine Rice ↓
So there is negative relation between price and quantity which implies that substitution effect is always negative.
Normal Good: If the consumption demand of a good increases when the income increases and vice- versa, then the good is called normal good. For normal good income effect is negative. Example: Fine rice. Fine rice is a good quality rice and when income increases we want to increase its consumption
Inferior Good: If the consumption demand of a good decreases when the income increases and vice- versa, then the good is called inferior good. For inferior good income effect is positive. Example: Coarse rice. Coarse rice is a bad quality rice and when income increases we want to decrease its consumption because we replace it with good quality rice like fine rice.