Question

economics

Problem 2 Jon is spending his money on potatoes (R) and all other goods (C). Suppose that the price of rice potatoes falls. Determine Jon's optimal consumption bundle using the tangency between his original budget line and one of his indifference curves as well as the consumption bundle after the price change, i.e., using the tangency between his new budget line and one of his indifference curves when 1. Potatoes is a normal good 2. Potatoes is an inferior good Decompose this total effect of a price change on his potatoes consumption into a substitution effect and an income effect. Under what condition, Jon would buy less potatoes as a result of the price change? (Hint: think about the relative magnitude of the effects)

Answer 1

Problem 2

1. Suppose the initial budget line is AB which is tangent to the initial indifference curve IC1 at point E1 with respect to which the optimal quantity of potatoes is X1. Now as the price of potatoes fall, the budget line rotates outward from AB to AC and the new budget line becomes tangent to the new indifference curve IC2 at point E3 with respect to which the new quantity of potatoes is X3. Now this total movement from E1 to E3 as a result of fall in price of potatoes can be decomposed into a substitution effect and an income effect.

Now to understand the substitution effect, we will hold the real income constant. Hence the consumer will stay on the initial indifference curve IC1, but as the price ratio has changed due to a fall in the price of potatoes, hence the consumer will stay on the budget line with it’s slope equal to the slope of the new budget line AC. Hence we draw a hypothetical budget line DE which is tangent to the initial indifference curve IC1 at point E2 and is parallel to the new budget line AC. Hence the movement from point E1 to E2 is the substitution effect due to which the quantity demanded of potatoes increase from X1 to X2. Now this substitution effect remains same for both the cases of when potatoes is a normal good and when potatoes is an inferior good.

Now in case 1 when potatoes is a normal good, now to understand the income effect, we will consider real income as variable. Now as the price of potatoes fall, consumers real income M/P increases I.e consumers purchasing power increases and consumers will feel richer, hence the budget line will shift rightward from DE to AC and the new budget line becomes tangent to the new indifference curve IC2 at point E3, with respect to which quantity demanded of potatoes increases from X2 to X3. Hence the movement from E2 to E3 along which quantity demanded of potatoes increases from X2 to X3 is the income effect when potatoes are normal good, Hence when potatoes are normal goods, both substitution and income effect lead to an increase in the quantity demanded of potatoes from x1 to X3. Hence, when potatoes are normal goods, John would buy more potatoes as a result of the price change.

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Now in case 2 when potatoes is an inferior  good, now to understand the income effect, we will consider real income as variable. Now as the price of potatoes fall, consumers real income M/P increases I.e consumers purchasing power increases and consumers will feel richer, hence the budget line will shift rightward from DE to AC and the new budget line becomes tangent to the new indifference curve IC2 at point E3, with respect to which quantity demanded of potatoes declines from X2 to X3. We know that in case of inferior goods, income elasticity of demand is less than zero which means that as consumers income increases, demand for the good decreases and vice versa. Hence the movement from point E2 to E3 along which the quantity demanded of potatoes decreases from X2 to X3 is the income effect. Now here in case of inferior goods, the substitution effect leads to increase in the quantity demanded of potatoes from X1 to X2 and the income effect leads to a decline in the quantity demanded of potatoes from X2 to X3. As the relative magnitude of income effect is greater than the magnitude of of the substitution effect, hence the quantity of potatoes will decline from X1 to X3 as a result of price change of potatoes and John would buy less potatoes as a result of the price change.

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