Question

3. Consider Charlie who consumes apples (xi) and bananas (2). Suppose that he consumes one apple and 8 bananas. That is, his current consumption bundle is (1,8). (a) Suppose that Charlie's marginal rate of substitution for one more apple is 2 bananas. If he is offered to trade apples and bananas at one-to-one rate, does he trade? Explain your answer. (b) Suppose that Charlie's preference is convex. If he were to consume 8 apples and one banana, his marginal rate of substitution would be (lower than, higher than, or the same as) 2 at the bundle (1,8). Explain your answer.

Answer 1

Answer (a) : Marginal Rate of substitution refers to the rate at which a consumer is willing to sacrifice one unit of a product in order to get one more unit of another product, thereby maintaining his same level of utility. In this case, Charlie consumes two products, apples (x1) and Bananas ( x2). His consumption bundle (i.e. the amount of the products he consumes to attain maximum satisfaction out of both the products) is given as (1 : 8 ) i.e. when Charlie consumes 1 unit of Apple and 8 units of Bananas, he gets totally satisfied. It is also given that Charlie’s marginal rate of substitution for one more unit of apple (i.e. after consumption of 1 unit of apple, the utility that Charlie derives from the consumption of the Second unit of Apple) is equal to the consumption of 2 bananas. This means, if after the consumption of the total 1 apple + 8 bananas, Charlie further consumes 1 apple or 2 bananas, he would be satisfied, or in other words, for consuming one more unit of apple, Charlie s ready to give up 2 bananas, or in order to consume 2 more unit of bananas, Charlie is ready to give up one unit of Apple. The Law of diminishing rate of marginal returns states that with the increased consumption of one good, his marginal rate of substitution of the good will decrease in comparison to the other good. i.e. Charlie initially consumes 1 apple and 8 bananas, but h is ready to give up one apple now for 2 more bananas, i.e. his marginal rate of substitute is decreasing. Since human nature always wants to search for t optimal equilibrium ( equilibrium rate of substitution means when the marginal of substitution for the both the products is the same ) , therefore Charlie will be ready to trade.

Answer (b) : If Charlie’s preferences are convex and he now consumes 8 apples and 1 banana, this means that in order to attain the equilibrium rate of marginal substitution, Charlie would have the desire to have more bananas than apples. The marginal rate of substitution for one apple will be lower than 2 at the bundle. This is because, earlier, Charlie consumed 8 bananas and only one apple. Thus, his desire for more apple made him to agree on substituting 2 bananas for it. However, now Charlie has 8 apples and only 1 banana, therefore, in order to have one more unit of apple, Charlie will no longer be ready to give up 2 bananas. He may be ready to give up lower units of bananas, may be 1 banana or half a banana or may be lower than that. This is because, the equilibrium rate of marginal rate of substitution states that every consumer wants to consume products at a level which satisfies him the most and much that he consumes both the products equally. Therefore, Charlie’s marginal rate of substitution would be lower than 2 at the bundle (1,8).