Marginal Utility, Utils Total Utility, Utils

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1 Mr Sydney Armstrong ECN 1100 Introduction to Microeconomics Lecture Note (5) Consumer Behaviour Evidence indicated that consumers can fulfill specific wants with succeeding units of a commodity but that each added unit provides less utility than the last unit purchased. A product has utility if it can satisfy a want: Utility is want-satisfying power. The utility of a good or service is the satisfaction or pleasure one gets from consuming it. Three characteristics of the concept must be emphasized: Utility and usefulness are not synonymous. Paintings by Picasso may offer great utility to art connoisseurs but are useless functionally (other than for hiding a crack on a wall). Implied in the first characteristic is the fact that utility is subjective. The utility of a specific product may vary widely from person to person. A jack-up truck may have great to someone who drives off-road but little utility to someone too old to climb into the rig. Eyeglasses have tremendous utility to someone who has poor eyesight but no utility at all to persons like Mr. Armstrong with 20/20 vision. Because utility is subjective, it is difficult to quantify. But for illustration purposes we assume that people can measure satisfaction with units called utils. Total Utility and Marginal Utility It is important for us to distinguish between total utility and marginal utility. Total utility is the total amount of satisfaction or pleasure a person derives from consuming some specific quantity. Marginal utility is the extra satisfaction a consumer realizes from an additional unit of that product. Alternatively, we can say that marginal utility is the change in total utility that results from the consumption of 1 more unit of a product. Mu = ΔTU/ΔQ Hot Dogs Consumed Total Utility, Utils Marginal Utility, Utils This information can be used to construct two graphs which are shown below.

2 35 Total Utility Total Utility Marginal Utility Marginal Utility Starting at the origin (from the graph or table), we observe that each of the first 5 units increases total utility (TU) but by a diminishing amount. Total utility reaches a maximum with the addition of the sixth unit and then decline. So in the graph and table above we find that marginal utility (MU) remains positive but diminishes through the first 5 units (while total utility increases but at a decreasing rate). Marginal utility is zero for the sixth unit (because that unit doesn t changes total utility). Marginal utility then becomes negative with the seventh unit and beyond (because total utility is falling). The table and graphs above tell us that each successive hot dog yield less extra utility, meaning fewer utils, than the preceding one as the consumer s wants for hot dog comes closer and closer to fulfillment. The principle that marginal utility declines as the consumer acquire additional units of a given product is known as the law of diminishing marginal utility. It is important to note that diminishing marginal utility always steps in after the first unit.

3 Consumer Choice and Budget Constraint In addition to explaining the law of demand, the idea of diminishing marginal utility explains how consumers allocate their money incomes among the many goods and services available for purchase. The typical consumer s situation has the following dimensions. Rational behavior The consumer is a rational person, who tries to use his or her money income to derive the greatest amount of satisfaction, or utility from it. Consumers want to get the most for their money or, technically, to maximize their utility. They engage in rational behavior. Preferences Each consumer has clear cut preferences for certain of the goods and services that are available in the market. We assume that buyers also have a good idea of how much marginal utility they will get from successive units of the various products they might purchase. Budget constraint At any point in time the consumer has fixed/ limited amount of money income. Since each consumer supplies a finite amount of human and property resources to society, he or she earns only limited income. Thus, every consumer faces what economists called a budget constraint (budget limitation), even those who earn millions of dollars a year. Of course, budget constraints are more severe for consumers with average incomes than for those with extraordinarily high incomes. Prices Goods are scares relative to the demand for them, so every good carries a price tag. We assume that the price tags are not affected by the amount of specific goods each person buys. Utility-Maximizing Rule Of all the different combinations of goods and services a consumer can obtain within his or her budget, which specific combination will yield the maximum utility or satisfaction? To maximize satisfaction, the consumer should allocate his or her money income so that the last dollar spent on each product yield the same amount of extra (marginal) utility. We call this the utility maximizing rule. When the consumer has balanced his or her margins using the rule, there is no incentive to alter the expenditure pattern. The consumer is in equilibrium and would be worse off if there were any alteration in the bundle of goods purchased, providing there is no change in taste, income, products or prices. Utility Maximizing Rule: MU of product A/ price of A = MU of product B/ Price of B MU of product Z/ Price of Z

4 Assume that John s income is $10 Product A: Price = $ 1 Product B: Price = $ 2 Unit of the product Marginal utility (A) Marginal Utility (B) First (1) Second (2) 8 20 Third (3) 7 18 Fourth (4) 6 16 Fifth (5) 5 12 Sixth (6) 4 6 Seventh (7) 3 4 Base on the table above which combination of product A and product B will maximize the consumer utility? Unit of the product Assume that John s income is $10 Product A: Price = $ 1 Product B: Price = $ 2 Marginal Marginal Utility Marginal utility (A) per Dollar Utility (B) (MU/price) (A) First (1) Second (2) Third (3) Fourth (4) Fifth (5) Sixth (6) Seventh (7) Marginal Utility per Dollar (MU/price) (B) From the table above, the utility maximizing combination of goods attainable by John is 2 units of A and 4 units of B Note that the marginal utility per dollar for both products is equal to 8. By summing the marginal utility information from column 2 and column 4, we find that John is obtaining 18 (10+8 =18) utils of satisfaction from 2 units of product A and 78 ( =78) utils of satisfaction form the 4 units of B. His 10 dollars optimally spent (1*2 + 2*4 = 10), yielding 96 utils of satisfaction (18+78 =96).

5 Note that there are two situations where the marginal utility per dollar for each product is equal at 10 and 6. Why these outcomes are inferior to the one above? First, when the marginal utility per dollar is equal to 10 for both products the first thing to note is that John is not spending all of his income, because at this point he is purchasing only 1 unit of product A with 2 units of product b which gives us 1*1 +2*2= 5. In this case he is only spending 5 dollars of his income. Apart from this his total utility is 54 utils that is 10 utils from the 1 unit of product A and 44 (24+20= 44) utils from the 2 units of product B which is less than 96 when compare to the combination above. Second, when the marginal utility per dollar for both products is equal to 6 the combination of product A and B at this point will produce a greater level of satisfaction than the previously discussed combinations, but given John s income of $10 this combination is unattainable. This is so because when the marginal utility per dollar for both products is 6 he would be purchasing 4 units of product A with 5 units of product B which gives us 1*4 + 2*5= 14. In essence to get this combination he would need an income of 14 dollars which he doesn t have. What is total utility at this point? What needs to happen in the following case to put the consumer into equilibrium when: MU of product A/ price A < MU of product B/ price B MU of product A/ price A > MU of product B/ Price B

6 Indifference Curve Analysis A more advance explanation of consumer behavior and equilibrium is based on: Budget lines Indifference curves The Budget Line: What is attainable A budget line (or, more technically, the budget constraint) is a schedule or curve that shows the various combinations of two products a consumer can purchase with a specific money income. If the price of product A is $ 1.50 and the price for product B is $ 1, a consumer can purchase all the combinations of A and B shown in the table below with the consumer money income being $12. At one extreme, the consumer might spend all of his or her income on 8 units of A and have nothing left to spend on B according to the table. Or, by giving up 2 units of A and thereby freeing up $3, the consumer could have 6 units of A and 3 units of B. And so on to the other extreme, at which the consumer could buy 12 units of B at $1 each, spending his or her entire money income on B with nothing left to spend on A. The Budget Line: whole-unit Combination of A and B Attainable with an Income of $12 Units of A (Price= $1.50) Units of B (Price= $1) Total Expenditure 8 0 $ 12 (= 12+0) 6 3 $12 (= 9+3) 4 6 $12 (=6+6) 2 9 $12 (=3+9) 0 12 $12 (=0+12) This information can be represented graphically as shown below, however the graph is not restricted to whole units of A and B as in the table. Every point on the graph represents a possible combination of A and B, including fractional quantities. Mathematically the budget line is derived by the following equation: Income = P x *Q x + P y *Q y

7 Product A Budget Line Product B The slope of the budget line measures the ration of the price of B to the price A; more precisely, the absolute value of the slope is PB/PA = $1/$1.50 = 2/3 or This is the mathematical way of saying that the consumer must forego 2 units of A (measured on the vertical axis) to buy 3 units of B (measured on the horizontal axis). In moving down the budget line, 2 units of A (at $1.50 each) must be given up to obtain 3 more units of B (at $1 each). This yields a slope of 2/3. The Budget line has two other significant characteristics: Income changes The location of the budget lines varies with money income. An increase in money income shifts the budget line to the right; a decrease in money income shifts the curve to the left. To verify this recalculate the table above, assuming that income is (a) $24 and (b) $6 and plot the new budget lines. Price changes A change in product price also shifts the budget line. A decline in the price of both products- equivalent of an increase in real income- shifts the curve to the right. Conversely, an increase in the prices of A and B shifts the curve to the left. Note what happens if the price of B changes while the price of A and income remain the same. If the price of B drops, the lower end of the budget line fans outward to the right. The opposite will happen if the price of B increases in this case the lower end of the budget line fans inwards to the left. In both instances the line remains anchored at 8 units on the vertical axis because the price of A has not changed.

8 Income increase Income Decrease Price A and B Decreases Price A and B Increases Price of B Decreases Price of B increases

9 Price of A Decreases Price of A Increases Indifference Curves What is preferred Budget lines reflect objective market data, specifically what income and prices. They reveal combinations of product A and product B that can be purchased, given current money income and prices. Indifference curves, on the other hand reflect subjective information about consumer preferences for A and B. An indifference curve shows all the combination of two products A and B that will yield the same level of satisfaction or total utility to a consumer. The table and graph below presents a hypothetical indifference curve for product A and B. The consumer s subjective preferences are such that he or she will realize the same total utility from each combination of A and B shown in the table or on the curve. So the consumer will be indifferent (will not care) as to which combination is actually obtained. An Indifference Schedule (Whole Units) Combination Units of A Units of B I 12 2 K 6 4 L 4 6 M 3 8

10 Product A 14 Indifference Curve Product B Indifference curves have three important characteristics: Indifference curves are Downwards sloping An indifference curve slopes downward because more of one product means less of the other if total utility is to remain unchanged. Suppose the consumer moves from one combination of A and B to another, say from J to K in the table and graph above. In so doing, the consumer obtains more of product B, increasing his or her total utility. But because total utility is the same everywhere on the curve, the consumer must give up some of product A, to reduce total utility by a precisely offsetting amount. Thus more of B necessitates less of A and the quantity of A and B are inversely related. A curve that reflects inversely related variables is downwards-sloping. Indifference Curves are Convex to the Origin A downward-sloping curve can be concave (bowed outwards) or convex (bowed inwards) to the origin. A concave curve has an increasing slope (steeper) slope as one move down the curve, while a convex curve has a diminishing (flatter) slope as one move down the curve. Note that the indifference curve is convex to the origin. Its slope diminishes or become flatter as we move from J to K to L, and so on down the curve. The slope of the indifference curve at each point is called the Marginal Rate of Substitution (MRS). The MRS shows the rate at which the consumer is willing to substitute one good foe another (in this case B for A) to remain equally satisfy. The diminishing slope of the indifference curve means that the willingness to substitute B for A diminishes as one move down the curve. MRS = Δ Y/ΔX

11 Indifference Curves Never Intersect Indifference curves identify a given level of satisfaction. Higher indifference curve mean higher level of satisfaction, lower indifference curves means lower levels of satisfaction. So when indifference curves intersect it would be difficult to identify on which curve the consumer is having a greater level of satisfaction. Indifference Map The single indifference curve as the one above reflects some constant (but unspecified) level of total utility or satisfaction. It is possible and useful to sketch a whole series of indifference curves or an indifference map, as shown below. Each curve reflects a different level of total utility. Specifically, each curve to the right of our curve (labeled I) reflects combinations of A and B that yield more utility than I. Each curve to the left of I reflects less total utility than I. As we move out from the origin, each successive indifference curve represents a higher level of utility. Quantity of A I Quantity of B Special Indifference Curves Quantity of A Perfect Substitutes Quantity of A Perfect Complements Quantity of B Quantity of B

12 Equilibrium at Tangency Since the axes for the budget line and indifference map are the same we can superimpose a budget line on the consumer s indifference map as shown below. By definition, a budget line indicates all the combinations of A and B that the consumer can attain with his or her money income, given the price of A and B. Of these attainable combinations, the consumer will prefer the combination that yields the greatest satisfaction or utility. Specifically, the utilitymaximizing combination will be the combination lying on the highest attainable indifference curve. It is called the consumer s equilibrium position. Quantity of A Y W 1 X I 3 I I 2 Q B1 Z Quantity of B In the graph above the consumer s equilibrium position is at point X, where the budget line is tangent to I. Why not point Y? Because Y is on a lower indifference curve I2. By moving down the budget line (by shifting dollars from purchases of A to purchases of B) the consumer can attain an indifference curve farther from the origin and thereby increase the total utility derived from the same income. Why not Z? For the same reason: Point Z is on a lower indifference curve I2. By moving up the budget line (by reallocating dollars from B to A) the consumer can get to higher indifference curve I and increase total utility. How about W on the indifference I3? While it is true that W would yield a greater total utility than X, point W is beyond (outside) the budget line and hence is not attainable by the consumer. Point X represents the optimal attainable combination of product A and B. Note that, according to the definition of tangency, the slope of the highest attainable indifference curve equals the slope of the budget line. Because the slope of the indifference curve reflects the MRS (marginal rate of substitution) and the slope of the budget line is PB/PA, the consumer s optimal or equilibrium position is the point where MRS = PB. PA

13 The Derivation of the Demand Curve The budget line determining the above equilibrium position assumes that money income is $12 and that PA = $1.5 and PB = $1. Let s see what happens to the equilibrium position when we increase PB to $1.5 and hold both money income and the price of A constant. The result is shown in the graph below. The budget line fans to the left, yielding a new equilibrium point X1 where it is tangent to the lower indifference curve I2. At X1 the consumer buys 2 units of B and 2 units of A. our interest is in B, and we now have sufficient information to locate two points on the demand curve for product B. We know that at equilibrium point X the price of B is $1 and the quantity purchased is 1 units; at equilibrium point X1 the price of B is $1.5 and 2 are purchased. By simple manipulation of the price of B in an indifference curve-budget line context, we have obtained a downward-sloping demand curve for B. We have thus again derived the law of demand assuming other things equal, since only the price of B was changed. Quantity of A 2 X1 X 1 I 3 I I 2 Q B2 Q B1 Quantity of B Price of B D 2 1 Quantity of B The notes came from McConnell &Brue, Economics, 15th edition, You are required to supplement this with additional reading.