Question

Imagine a representative consumer, whose utility for apples (X) and all other goods (Y) can be represented in a Cobb-Douglas form. 1. Please graphically represent consumer indifference curves, given prices Px and Py and the budget constraint M. 2. What will happen to consumer utility and optimal bundle if consumer income (budget) increases and apples are a necessity good? Please show graphically and explain the intuition. 3. What will happen to consumer utility and optimal bundle if apple price decreases and apples are an inferior good? Please show graphically and explain the intuition. 4. Finally, explain how you would derive demand curves from point 1 and point 3? Graphically show consumer surplus and compare it for the original scenario, and the one in point 3.

True or False 1. The decisions of consumer and firms in market is the government. 2. According to the Law of Demand, the demand curve for a good will shift rightward when the price of the good increases. 3. The marginal rate of transformation of y for x represents the rate at which the consumer must give up x to get one more y. 4. The substitution effect can be measured holding income constant

Answer 1

Ans-2 when income increases M to M'. BL shift rightward to BL'. Slope remains same because price are same. Now consumer have more income to spend on goods so he will be on higher IC i.e IC'. Consumption of both goods increases and apples are necessity good so when income increases demand of necessity good increases.

Ans-3 when price of x falls i.e a inferior good. We will take this price effect in two steps 1. Substitution effect is change in demand due to change in relative price keeping purchasing power constant. In this we will pivot BL around original bundle A BL to BL'. Substitution effect is always negative so price fall will increase demand of x to x' at point B. Income effect calculated by keeping relative price constant increase purchasing power BL' to BL''. As income effect is negative for inferior good increase in income due to price fall lead to decrease demand of x, from x' to x". So final movement we can see is from x to x" is positive so his utility will increase and demand of both goods increase.

Ans-4 price offer curve POC is the demand curve of goods. If label those points in other diagram called demand curve. At px it's consuming x and at px' ( px > px' ) it's consuming x" . So by connecting points we get demand curve for x (apples).

ABC area in consumer surplus when price is px point 1 and ADE area is consumer surplus when price is px' point 3. ∆ADE > ∆ABC so consumer surplus greater at point 3