Kevin has well-behaved preferences and currently has a bundle with positive amounts of two goods. Let...

Kevin has well-behaved preferences and currently has a bundle with positive amounts of two goods. Let x1 and x2 denote the quantities of goods 1 and 2, respectively. Thinking in terms of x1 on the horizontal axis, the absolute value of Kevin’s marginal rate of substitution between the two goods at his current consumption bundle is greater than 3. Using this information, can the theory we have developed so far predict Kevin’s reaction to the following propositions? (Please show all work and explain everything)

(a) ”I give you a bit of x1 and you give me 3 units of x2 for each unit of x1.”

(b) ”You give me a little of x1 and I give you 3 units of x2 per unit of x1.”

Expert Solution

Given that x1 and x2 denote the quantities of goods 1 and 2. Now x1 is on the horizontal axis and x2 is on the vertical axis, the absolute value of Kevin’s marginal rate of substitution between the two goods at his current consumption bundle is greater than 3.

(a) ”I give you a bit of x1 and you give me 3 units of x2 for each unit of x1.”

Kevin is willing to trade more than 3 units of x2 with 1 unit of x1. Hence when he is offered to pay 3 units of x2 for each unit of x1, he may or may not accept. This is because going towards left of the current bundle (increasing x1 and decreasing x2) will have smaller MRS but we do not know if MRS will still be higher than 3 or not. And so Kevin will or will not be willing to trade 1 unit of x1 for 3 units of x2.

(b) ”You give me a little of x1 and I give you 3 units of x2 per unit of x1.”

MRS is > 3 which means Kevin is willing to trade more than 3 units of x2 with 1 unit of x1. Otherwise he can pay 1 unit of x1 for a quantity of x2 more than 3 units. Hence when he is offered to receive 3 units of x2 for each unit of x1, he will not accept. This is true because going towards right of the current bundle (reducing x1 and increasing x2) will have higehr MRS and so Kevin will be willing to trade 1 unit of x1 for more than 3 units of x2

Rahul Sunny answered 1 year ago

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