Review Questions IV – Fall 2011 With Answers 1. As discussed in class, what are the three axioms that lay the foundation for the theory of the consumer? Completeness, Non‐satiation, Transitivity – these axioms are discussed in detail in the text and in class notes. 2. If goods A&B have strictly positive marginal value to the individual, can indifference curves be upward sloping? Horizontal? Vertical? The answer to all three questions is “NO”. In each case, the axiom of non‐satiation would be violated ….. 3. How is the marginal rate of substitution of good B for good A related to the slop of the indifference curve? As shown in class, the MRS of good B for good A can be shown to equal the “negative of the slope of the indifference curve” and equal to the MU of good B divided by the MU of good A. 4. How is convexity of indifference curves related to the marginal rate of substitution? Convexity implies the slope declines as good B is substituted for Good A. This implies convexity depends on a declining MRS of good B for Good A. 5. What is the equal marginal principle? How is this principle derived from the constrained optimization problem? Equal Marginal Principle ‐ MUa/Pa = MUb/Pb. Note that a better description of the principle would be the “equal marginal per dollar spent principle.” As shown in class, this principle follows from the observation that the optimal bundle for consumption is a point of tangency between the indifference curve and the budget line. It then follows that this point of tangency is where the MRS of good B for good A equals the negative of the slope of the budget line, which is equal to the Pb/Pa. 6. Using indifference curves and budget lines for a two good scenario, show why an increase in income must imply at least one good is a normal good. Your graph would show an indifference curve mapping, with several budgets lines that shift outward as income increases. The optimal bundle would change as income increases. if income is increasing, expenditures must increase for at least one of the goods. 7. If the price good B falls and expenditures on good B increase, what do we know about the elasticity of demand for good B? In a two good world, in this scenario, what must happen to the quantity of good A purchased and expenditures on good A? We know from our earlier discussions that if Pb falls and total expenditures on good B increase, then the elasticity of demand for Good B is greater than one for that price change. It also follows that, ceteris paribus, if a price change leads to greater total expenditures on good B, then expenditures on good A must fall. One would simply have less income to spend on Good A, if expenditures on good B increase.