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Microeconomic Foundation of Macroeconomics This Handout Is Handout A: Microeconomic Foundation of Macroeconomics This handout is concerned with microeconomics foundation for macroeconomics. In particular we focus on the Theory of Consumer Choice, or consumer theory for short. The goal is to understand how a consumer makes choices with a given preference and budget constraint. Budget Constraint Consider two goods: Apple (A) and Banana (B). Denote their quantities by and ; prices by and The budget constraint is where denotes the income. Equation (1) can be rewritten as ( ) ( ) We can draw the budget line using (2). We put on the vertical axis, and on horizontal axis. The intercept of the budget line is____________________ The slope of the budget line is ____________________ The maximum amount of is 1 The maximum amount of is The budget line looks like Exercise 1: After falls, the intercept (rises falls) and the absolute value of slope (rises falls). So the budget line shifts (inward outward) Exercise 2: What happens to the maximum amount of after falls? Exercise 3: What happens to the budget line when Y rises? Preference The preference of the consumer is captured by his utility function . Denote the marginal utility (MU) by 2 measures the change in utility when changes by a small amount. We assume utility rises when either more apples or more bananas are consumed, i.e., Moreover we assume decreasing marginal utility (DMU) DMU says that as more and more apples (bananas) are consumed, the additional utility brought by the last apple (banana) becomes less and less. In other words as more goods are consumed total utility rises but at decreasing rate. Intuitively, DMU is due to the fact that people prefer diversity. Indifference Curve A consumer’s preference can also be described by indifference curve. By definition, an indifference curve shows the bundles of consumption that make the consumer equally happy, or equivalently, bundles of goods that give the consumer the same level of utility. Consider a given level of utility ̅: ̅ Taking total differentiation of (6) yields 3 ̅ The last equality in (7) is due to the fact that ̅ is fixed when we move along a given indifference curve. Equation (7) can be rewritten as The slope of the indifference curve is . Equation (8) shows that the slope is (positive negative), so indifference curve is (downward upward) sloping. That means the consumer must consume more bananas as he consumes fewer apples in order to maintain the level of happiness. Formally we call the slope of indifference curve the marginal rate of substitution (MRS). MRS measures how many apples the consumer requires to be compensated for a one-unit reduction in banana consumption. Put differently MRS measures how many apples a consumer is willing to trade for one unit of banana. Next we show MRS has certain property. Suppose falls, DMU (5) implies that (rises falls) To make consumer equally happy, must (rise fall) when falls. This change in implies that (rises falls). Thus equation (8) indicates that the absolute value of MRS (rises falls) when falls and rises. In other words, the 4 indifference curve gets (steeper flatter) when falls and rises. Now we reach the below conclusion The indifference curve is convex (bowed inward). Intuitively, the indifference curve is convex because people are more willing to trade away goods that they have in abundance and less willing to trade away goods of which they have little. When a person has many apples, he is willing to trade, say, 10 apples for 1 banana. In contrast when he has many bananas, he is willing to trade 1 apple for 10 bananas. Optimal Choice The goal of a consumer is to find the optimal bundle of apples and bananas (optimum) given his preference and budget. Mathematically the consumer tries to solve the below constraint optimization problem: We can transform this constraint optimization problem into an unconstraint optimization problem by substituting (2) into the objective function: ( ) Taking derivative of (9’) with respect to and letting the derivative equal zero lead to the first order condition (FOC): 5 Equation (10) gives hints about how to find optimum using graphs. The answer is the optimum is located where the budget line is tangent to the indifference curve. To see this, Step 1: the slope of budget line is___________ Step 2: the slope of indifference curve is_____________ Step 3: at the tangent point, the two slopes ______________ The graph looks like: Exercise: show that utility is not maximized and can be increased when (10) is violated. More explicitly, consider the case where Step1: utility decreases by ______ when one unit of apple is given up. Step 2: on market, one unit of apply can be traded for ___banana. Step 3: the amount of banana in step 2 can increase utility by____ Step 4: the reduction of utility in step 1 is (more less) than the increase of utility in step 3. So overall the utility (rises falls) if the consumer trades apple for banana. 6 Homework: show how to increase utility if Therefore the FOC (10) has a simple interpretation: at the optimum, the marginal utility per dollar spent on good A should equal the marginal utility per dollar spent on good B. If not, the consumer can increase utility by spending less on the good that provides lower marginal utility per dollar and more on the good that provides higher marginal utility per dollar. Income Effect and Substitution Effect Now we are ready to analyze the effect of change in price on consumption. The total effect of price change is the sum of income effect and substitution effect. Income effect is the change in consumption that results when a price change moves the consumer to a higher or lower indifference curve. Substitution effect is the change in consumption that results when a price change moves the consumption along a given indifference curve to a point with a new marginal rate of substitution. For example, suppose the apple price falls. Step 1: label the tangent point (optimum 1) of budget line and indifference curve as point 1. 7 Step 2. falling apple price causes the budget line to shift (inward outward). Step 3. label the tangent point (optimum 2) of new budget line and new indifference curve as point 2. The indifference curve where point 2 is located must give consumer higher utility than point 1. Why? Now draw a hypothetical budget line that is parallel to the new budget line and tangent with the old indifference curve at point 3. The movement from point 1 to point 3 is substitution effect because we move along a given indifference curve The movement from point 3 to point 2 is income effect because we move to a new indifference curve Consider substitution effect first. The substitution effect on apple is positive, i.e., consumer buys more apples since apples become relatively cheap. Now let’s turn to income effect. Falling price has the same effect as rising income in terms of giving rise to higher purchasing power. If we assume apple is a normal good, i.e., its consumption rises when income rises, then the income effect on apple is positive. Because substitution and income effects act in the same direction (both are positive), consumer buys more apples for 8 sure after apple price falls. Hence the demand curve for apple is downward-sloping. Exercise: now consider how falling apple price affects banana consumption. Step 1: falling apple price makes banana relatively (cheap expensive) and consumers wants to buy (more less) banana. So substitution effect on banana is (positive negative). Step 2: falling apple price makes consumer feels (richer poorer). If we assume banana is a normal good, then income effect on banana is (positive negative). Step 3: income and substitution effects act in (same opposite) direction for banana. So the total effect on banana can be either positive or negative (ambiguous), depending on which effect is bigger (dominates). Homework An inferior good has negative income effect, i.e., its consumption falls when income rises. A Giffen good is an extreme inferior good for which the income effect dominates the substitution effect. Please draw graph to show as the price of a Giffen good falls, its consumption falls. This means the demand curve for Giffen good is upward-sloping. Application 1 of Consumer Theory: Labor Supply Curve Here we want to apply the consumer theory to analyze how a person decides to allocate time between work and leisure. 9 In this case the two goods are consumption and leisure. We assume both are normal goods. Suppose the real wage rises. This, in effect, makes the price of consumption to fall. Why? Warning: you cannot think of wage as the price of leisure. You earn wage, not pay it. Now consider the total effect of falling consumption price. The income effect for consumption is positive The substitution effect for consumption is positive So the person definitely has more consumption after his wage rises. On the other hand, the income effect for leisure is ______ The substitution effect for leisure is _________ So the total effect of change in wage on leisure is _________. If we assume substitution effect dominates the income effect, then the person will have less leisure and will work more hours after wage rises. Under this assumption, the labor supply curve is upward-sloping. Empirical data, however, suggests that the labor supply curve can be downward-sloping. Application 2 of Consumer Theory: Intertemporal Choice Here we focus on how a person makes decision of consumption vs. saving over time. 10 For simplicity, assume a person lives only two periods: t=1 (young) and t=2 (old).
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