712topic03 - Topic #3 General Equilibrium Our consumer...

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Topic #3 General Equilibrium Our consumer theory will have a framing premise and three assumptions. A framing premise is something that can’t be proven – it’s either accepted or rejected. Our framing premise is that individuals are self-interested. That is, they act to be made as well off as possible under the circumstances. Further, our consumers are rational and goal-directed. We assume that they act in a purposeful manner. This does not mean that our consumers are selfish . Being self-interested does not mean you benefit from depriving others. For example, let Carol’s ordinal utility be represented by the following equation, U = F + B, where F is footballs and B is books. An indifference curve connects all the consumption bundles that generate the same level of utility. Thus, a consumer is indifferent among the consumption bundles on a particular indifference curve. For example, the following indifference curves represents X units of utility. Higher indifference curves yield more utility. Thus, consumption bundles to the north-east are superior bundles and consumption bundles to the south-west are inferior bundles. Footballs Figure 1 SUPERIOR BUNDLES 36 a d b 16 INFERIOR c BUNDLES 1 4 16 49 Books In addition, our theory has three assumptions: 1. Completeness - the consumer has and can rank in order of preference all consumption items. No flipping of coins or enemeneminemo. 2. Transitivity - preferences are rational and consistent. No rock, paper, scissors. The following indifference map violates the assumption of transitivity. For example, try to rank consumption bundles a, b, and c. Consumption Good Y a c b Consumption Good X
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It appears that a>b, a=c, and b=c, which does not make sense. So, we conclude that indifference curves can't intersect. 3. Nonsatiation - more is preferred to less. This means that indifference curves can’t be positively sloped and that indifference curves can’t be fat. The Marginal Rate of Substitution (MRS YX ) is the amount of the consumption good measured on the Y axis that an individual would be willing to give up in order to obtain another unit of the consumption good measured on the X axis. We assume that the marginal rate of substitution is diminishing as we move from left to right along an indifference curve. This makes indifference curves convex. For example MRS FB is the maximum amount of footballs the consumer is willing to give up to obtain another book. Find the MRS between bundles “a” and “b” and “b” and “c”. Does the MRS increase or decreases as we move from left to right? Suppose consumption bundle “e” has 49 footballs and 1 book. Calculate the MRS between “e” and “a”. Footballs Figure 1 36 a b 16 c 1 16 49 Books Formally, ∆U = MU F (∆F) + MU B (∆B). Since utility is constant along an indifference curve, 0 = MU F (∆F) + MU B (∆B) when calculating MRS. Thus, MU B /MU F = ∆F/∆B. To see why the MRS is diminishing, suppose I give you 10 large pizzas (each with 10
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712topic03 - Topic #3 General Equilibrium Our consumer...

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