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EC130 Foundations of Economic Analysis, 2004-5. Notes and OHPs, Topic 3. OHP32 EC130 FOUNDATIONS OF ECONOMIC ANALYSIS 2004- 2005 DEPARTMENT OF ECONOMICS UNIVERSITY OF WARWICK Topic 3 • Preferences and Constraints • Utility Maximisation • Income and Substitution Effects • Application to the Supply of Labour • Market Demand Curves 1 EC130 Foundations of Economic Analysis, 2004-5. Notes and OHPs, Topic 3. OHP33 • Preferences and Constraints Preferences Suppose your happiness just depends on two items: Books and Food. We assume that you have preferences over books and food and that these preferences satisfy various axioms, such as: • Non-satiation Books B1 F1 2 F2 Food EC130 Foundations of Economic Analysis, 2004-5. Notes and OHPs, Topic 3. OHP34 • Ordinal ranking • Transitivity If some basket or 'bundle' of goods, say α, is preferred to some other, say β, and if β is preferred to a further bundle, say ρ, then it follows by transitivity that α is preferred to ρ. This is regarded as a necessary axiom for consumers to be thought of as 'rational'. We write it as: Similarly, transitivity pertains to indifference . . . • Completeness This means that any two bundles can be compared (no matter how far apart or how close together): Books B1 F1 3 Food EC130 Foundations of Economic Analysis, 2004-5. Notes and OHPs, Topic 3. OHP35 Axioms like these enable us to represent individuals' preferences diagrammatically with what are called 'indifference curves'. It follows from the axioms about preferences that indifference curves will have the following key properties: • Slope downwards • Every point in the diagram will lie on a (unique) indifference curve • Indifference curves cannot cross Let us see why these properties obtain. Figure 3.1 Books B1 F1 Food Hence, indifference curves slope downwards. 4 EC130 Foundations of Economic Analysis, 2004-5. Notes and OHPs, Topic 3. OHP36 Figure 3.2 Books I2 I1 Food Hence, indifference curves cannot cross. 5 EC130 Foundations of Economic Analysis, 2004-5. Notes and OHPs, Topic 3. OHP37 If we now add one further assumption about the nature of preferences - the assumption of the diminishing marginal rate of substitution - then we also know that indifference cures must have a further property: they must be convex to the origin. Figure 3.3 Books Food The marginal rate of substitution (MRS) tells us how many more books we would need to make up for (ie to leave our level of happiness/utility unaffected by) the loss of one unit of food. The MRS is diminishing if it is the case that the less food we have, the greater the number of extra books we would need to compensate for the loss of a given amount of food (the example of diamonds and water is often used here). 6 EC130 Foundations of Economic Analysis, 2004-5. Notes and OHPs, Topic 3. OHP38 Thus, we have the idea of indifference curves to represent consumer 'utility'. Furthermore, we assume that the consumer will try to obtain the highest level of utility possible: Figure 3.4 Books Food The capacity of the consumer to raise their utility depends upon . . . . . . . . their budget constraint. 7 EC130 Foundations of Economic Analysis, 2004-5. Notes and OHPs, Topic 3. OHP39 The budget constraint Figure 3.5 Y M = px X + p yY X Total expenditure, E, must not exceed total money income, M. Or: E = px X + p yY ≤ M , where Y is the number of books bought and X is the amount of food. In the absence of savings, we can write this as: M = px X + p yY 8 EC130 Foundations of Economic Analysis, 2004-5. Notes and OHPs, Topic 3. OHP40 In the diagrams we have been drawing in (X,Y)-space, the equation for the budget constraint can be represented as: Figure 3.6 Y M = px X + p yY M py M px X To see why the intercepts have the values they do, notice that the budget equation can be re-written as: Y = (M − px ) / p y From this, you can work out the slope of the budget equation . . . do it! Hence, you can tell how the budget constraint moves when: • Money income increases • Price of food rises • Price of books falls • Price of food and books rises by the same percent • Money income and both prices all rise by 10% Show each of these in a diagram. 9 EC130 Foundations of Economic Analysis, 2004-5. Notes and OHPs, Topic 3. OHP41 Now we can bring together the analysis of indifference curves and that of the budget constraint, and thereby see what will determine the consumer's 'utility-maximising' equilibrium: Figure 3.7 Y Consumer Equilibrium . . . why? X Notice that in the consumer equilibrium, the budget line is a tangent to the indifference curve. I.e., the two slopes are equal: thus, the MRS = price ratio. With this model of consumer behaviour, we can work out how the consumer might respond to changes in income and/or price . . . 10 EC130 Foundations of Economic Analysis, 2004-5. Notes and OHPs, Topic 3. OHP42 Consider first changes in income: Effects of changes equilibrium. Figure 3.8 in income on consumer What happens to the consumer's optimising point when income falls? Y X Note that the fall in money income is represented by a parallel shift inwards of the budget line. • What happens to the level of demand for X and Y? • Draw the new optimising point. • Connect the original and new optima and hence derive the ICC. • Distinguish between normal and inferior goods. Also, think about the income elasticity of demand (and about luxury and necessary goods). 11 EC130 Foundations of Economic Analysis, 2004-5. Notes and OHPs, Topic 3. OHP43 Effects of changes in price on consumer equilibrium. Figure 3.9 What happens to the consumer's optimising point when price of X falls? Y X Note that the fall in the price of X is represented by an outward rotation of the budget line: why? • What happens to the level of demand for X and Y? • Draw the new optimising point (must it be to the right of the original?). • Connect the original and new optima and hence derive the PCC. • Distinguish between substitutes and complements. 12 EC130 Foundations of Economic Analysis, 2004-5. Notes and OHPs, Topic 3. OHP44 Figure 3.10 We can now derive a demand curve from first principles. We do this by plotting the PCC into a diagram with price and quantity axes: Y PCC M/Px1 M/Px2 X PX Now just show prices on this lower diagram and hence plot the demand curve. X1 X2 13 X EC130 Foundations of Economic Analysis, 2004-5. Notes and OHPs, Topic 3. OHP45 The demand curve we have just derived is called the Constant Money Income Demand Curve (CMIDC). • Why? • Must it always have a negative slope? Typically the CMIDC has a negative slope: as the price of a good falls, ceteris paribus, the demand for it rises. This is because two effects are going on when the price falls. First, the lower price means it is now cheaper relative to the other good than was previously the case. This generates a substitution effect. Second, with the lower price, the consumer is better off and so can afford more of all goods (look at the diagram again). This is called the income effect. We can try to distinguish between the income and substitution effects in a diagram: 14 EC130 Foundations of Economic Analysis, 2004-5. Notes and OHPs, Topic 3. OHP46 Distinguishing between the income and substitution effects. Y To see the substitution effect of the price fall on the demand for X, shift B2 back in a parallel way until it just touches I1 I1 B1 B2 X Y The income effect of the price fall is then the remainder of the total effect. To see this, just plot the new optimum on B2 I1 S X1 B1 B2 X X2 15 EC130 Foundations of Economic Analysis, 2004-5. Notes and OHPs, Topic 3. We know that if we plot from the PCC in (X, Y)-space into the diagram in (PX, X)-space, we can derive the CMIDC. That is, the CMIDC tells us the total effect of a price change on the demand for X: made up of both the income and substitution effects. If instead, we just consider the substitution effect and plot the resulting demand curve, we obtain the CRIDC: Constant real income demand curve. This is the demand curve derived when we consider the effect of a price change, but exclude the income effect. As it just traces out the substitution effect, it moves us along the initial indifference curve. Thus, utility is held constant. As utility is a measure of real income, the resulting demand curve is called the CRIDC. (Notice that money income is not held constant along the initial indifference curve as we trace out the substitution effect. Rather, it is as though we are giving the consumer a price fall with one hand, but taking away money income with the other so as to keep their level of utility constant.) To see the CRIDC diagrammatically, just plot down from the substitution effect in the previous diagram into the (PX, X) diagram. Then compare the CMIDC and the CRIDC. • We said CMIDC could have a positive slope. Is this true of CRIDC? • Which of the two demand curves is the more elastic? Why? What does this depend on? 16 EC130 Foundations of Economic Analysis, 2004-5. Notes and OHPs, Topic 3. • What is a Giffen good? How is it related to an inferior good? In lectures, we then consider market demand curves. And then an application of this analysis to the important issue of labour supply. 17