MANAGERIAL ECONOMICS II: DEMAND AND SUPPLY Introduction Demand theory is one of the core theories of microeconomics and consumer behaviour. It attempts at answering questions regarding the magnitude of demand for a product or service based on its importance to human wants. It also attempts to assess how demand is impacted by changes in prices and income levels and consumers preferences/utility. Based on the perceived utility of goods and services to consumers, companies are able to adjust the supply available and the prices charged. Introduction...... In economics, demand has a specific meaning distinct from its ordinary usage. In common language we treat ‘demand’ and ‘desire’ as synonymously. This is incongruent from its use in economics. In economics, demand refers to effective demand which implies three things: • Desire for a commodity • Sufficient money to purchase the commodity, rather the ability to pay • Willingness to spend money to acquire that commodity Introduction...... The following should also be noted about demand: • Demand always alludes to demand at price. The term ‘demand’ has no meaning unless it is related to price. For instance, the statement, 'the weekly demand for potatoes in city X is 10,000 kilograms' has no meaning unless we specify the price at which this quantity is demanded. • Demand always implies demand per unit of time. Therefore, it is vital to specify the period for which the commodity is demanded. For instance, the statement that demand for potatoes in city X at birr 8 per kilogram is 10,000 kilograms again has no meaning, unless we state the period for which the quantity is being demanded. Introduction...... A complete statement would therefore be as follows: ‘The weekly demand for potatoes in September 2016 in Addis Ababa at birr 8 per kilogram was 10,000 kilograms'. It is necessary to specify the period and the price because demand for a commodity will be different at different prices of that commodity and for different periods of time. • The demand must relate to a specific market as well Thus, we can define demand as follows: “The demand for a commodity at a given price is the amount of it which will be bought per unit of time at that price at a particular market”. The Law of Demand We have considered various factors that fashion the demand for a commodity. As explained the first and the most important factor that determines the demand of a commodity is its price. If all other factors (noted above) remain constant, it may be said that as the price of a commodity increases, its demand decreases and as the price of a commodity decreases its demand increases. This is a general behaviour observed in a market. This gives us the law of demand: The law of demand states that “the quantity demanded of a good or service is inversely related to the selling price, ceteris paribus”. The law of demand..... The demand curve Symbolically, the law of demand may be summarised as: and The above equation states that QD, the quantity demanded of a good or service, is functionally related to the selling price P. The Inequality sign asserts that quantity demanded and price are inversely related. This relationship is illustrated in the demand curve. The downward-sloping demand curve illustrates the inverse relationship between the quantity demanded of a good or service and its selling price. The law of demand..... Assumptions of the Law of Demand 1. Income level should remain constant: The law of demand operates only when the income level of the buyer remains constant. If the income rises while the price of the commodity does not fall, it is quite likely that the demand may increase. Therefore, stability in income is an essential condition for the operation of the law of demand. 2. Tastes of the buyer should not alter: Any alteration that takes place in the taste of the consumers will in all probability thwart the working of the law of demand. It often happens that when tastes or fashions change people revise their preferences. As a consequence, the demand for the commodity which goes down the preference scale of the consumers declines even though its price does not change. The law of demand..... 3. Prices of other goods should remain constant: Changes in the prices of other goods often impinge on the demand for a particular commodity. If prices of commodities for which demand is inelastic rise, the demand for a commodity other than these in all probability will decline even though there may not be any change in its price. Therefore, for the law of demand to operate it is imperative that prices of other goods do not change. 4. No new substitutes for the commodity: If some new substitutes for a commodity appear in the market, its demand generally declines. This is quite natural, because with the availability of new substitutes some buyers will be attracted towards new products and the demand for the older product will fall even though price remains unchanged. Hence, the law of demand operates only when the market for a commodity is not threatened by new substitutes. The law of demand..... 5. Price rise in future should not be expected: If the buyers of a commodity expect that its price will rise in future they raise its demand in response to an initial price rise. This behaviour of buyers violates the law of demand. Therefore, for the operation of the law of demand it is necessary that there must not be any expectations of price rise in the future. 6. Advertising expenditure should remain the same: If the advertising expenditure of a firm increases, the consumers may be tempted to buy more of its product. Therefore, the advertising expenditure on the good under consideration is taken to be constant. The law of demand..... Why does the demand curve slope downwards? The reasons behind the law of demand i.e. inverse relationship between price and quantity demanded are following: • Substitution Effect: When the price of a commodity falls it becomes relatively cheaper if price of all other related goods, particularly of substitutes, remain constant. In other words, substitute goods become relatively costlier. Since consumers substitute cheaper goods for costlier ones, demand for the relatively cheaper commodity increases. The increase in demand on account of this factor is known as substitution effect. The law of demand..... • Income Effect: As a result of fall in the price of a commodity, the real income of its consumer increase at least in terms of this commodity. In other words, his/her purchasing power increases since she/he is required to pay less for the same quantity. The increase in real income (or purchasing power) encourages demand for the commodity with reduced price. The increase in demand on account of increase in real income is known as income effect. It should however be noted that the income effect is negative in case of inferior goods. The law of demand..... • Diminishing Marginal Utility: Diminishing marginal utility as well is to be held responsible for the rise in demand for a product when its price declines. When an individual purchases a product, She/he swaps Her/his money revenue with the product in order to increase their satisfaction. She/He continues to purchase goods and services as long as the marginal utility of money (MUm) is lesser than the marginal utility of the commodity (MUc). Given the price of a commodity, they modify their purchase so that MUc = MUm. The law of demand..... This plan works well under both Marshallian assumption of constant MUm as well as Hicksian assumption of diminishing MUm. When price falls, (MUm = Pc) < MUc. Thus, equilibrium state is upset. To get back his equilibrium state, i.e., MUm = PC, = MUC, he buys more quantities of the commodity. For, when the supply of a commodity rises, its MU falls and once again MUm = MUC. For this reason, demand for a product rises when its price falls. The law of demand..... Exceptions to the Law of Demand • Apprehensions about the future price: When consumers anticipate a constant rise in the price of a long-lasting commodity, they purchase more of it despite the price rise. They do so with the intention of avoiding the blow of still higher prices in the future. Likewise, when consumers expect a substantial fall in the price in the future, they delay their purchases and hold on for the price to decrease to the anticipated level instead of purchasing the commodity as soon as its price decreases. These kinds of choices made by the consumers are in contradiction of the law of demand. • Status goods: The law does not concern the commodities which function as a ‘status symbol’, add to the social status or exhibit prosperity and opulence e.g. gold, precious stones, rare paintings and antiques, etc. Rich people mostly purchase such goods as they are very costly. THE MARKET DEMAND CURVE The quantity of a commodity which an individual is willing to buy at a particular price of the commodity during a specific time period, given his money income, his taste and prices of substitutes and complements, is known as individual demand for a commodity. The total quantity which all the consumers of a commodity are willing to buy at a given price per time unit, other things remaining the same, is known as market demand for the commodity. In other words, the market demand for a commodity is the sum of individual demands by all the consumers (or buyers) of the commodity, per time unit and at a given price, other factors remaining the same. The Market Demand Curve..... Table: Price and Quantity Demanded The Market Demand Curve..... The law of demand is a theoretical explanation of the expected behaviour of individual economic units when confronted with a change in the price of a commodity. The individual demands for commodity X are given by DA, DB and Dc, respectively. The horizontal summation of these individual demand curves results into the market demand curve (DM) for the commodity X. The curve DM represents the market demand curve for commodity X when there are only three consumers of the commodity. The Market Demand Curve is the Horizontal Summation of Individual Demand Curves. THE DEMAND FUNCTION The functional relationship between the demand for a commodity and its various determinants may be expressed mathematically in terms of a demand function, thus: Dx = f (Px, Py, M, T, A, U) where, • • • • • • • • Dx = Quantity demanded for commodity X. f = functional relation. Px = The price of commodity X. Py = The price of substitutes and complementary goods. M = The money income of the consumer. T = The taste of the consumer. A = The advertisement effects. U = Unknown variables or influences. The demand function... The above-stated demand function is a complicated one. Again, factors like tastes and unknown influences are not quantifiable. Economists, therefore, adopt a very simple statement of demand function, assuming all other variables, except price, to be constant. Thus, an over-simplified and the most commonly stated demand function is: Dx = f (Px), which connotes that the demand for commodity X is the function of its price. The traditional demand theory deals with this demand function specifically. The demand function... Let us consider three hypothetical individual demand functions for a product: QD,1=a1+b1P...........................a QD,2=a2+b2P............................b QD,3=a3+b3P............................c where the QD,i terms represent the individual’s demand for the commodity, the ai terms are positive constants, and the bi terms the unit change in quantity demanded given a change in the selling price. The demand function... For any given price, the market demand curve is the sum of the horizontal distances from the vertical axis to each individual demand curve. Summing together the above equations ( a,b, and c) we get: QD,1 +QD,2 +QD,3 = (a1 + a2 + a3 ) + (b1 + b2 + b3 )P Or QD = a + bP where a = a1+ a2 + a3 and b = b1+ b2 + b3. In general, for the consumer case: where QD,M is market demand The demand function... Problem : Suppose that the total market demand for a product comprises the demand of three individuals with identical demand equations. QD,1 =QD,2 =QD,3 = 50 - 25P a) What is the market demand equation for this product? b) Draw the market demand curve. The demand function... Solution: The market demand curve is the horizontal summation of the individual demand curves. The market demand equation is: QD=Qd1+Qd2+Qd3= (50 - 25P)+(50 - 25P)+(50 - 25P)=150 - 75P The demand function... Problem: Suppose that the total market demand for a product consists of the demands of individual 1 and individual 2. The demand equations of the two individuals are given by the following equations: Qd1=20-2p and Qd2=40-5p a) What is the market demand equation for this product? b) Draw the market demand curve. OTHER DETERMINANTS OF MARKET DEMAND Other demand determinants include income, consumer preferences, the prices of related goods, price expectations, and population. Shifts in a price-demand curve may take place owing to the change in one or more of other determinants of demand. OTHER DETERMINANTS OF MARKET DEMAND…… OTHER DETERMINANTS OF MARKET DEMAND….. Market demand curve Consisting the all determinant variables: Dx = f (Px, Py, M, T, A, E, U) where, • • • • • • • • • Dx = Quantity demanded for commodity X. f = functional relation. Px = The price of commodity X. Py = The price of substitutes and complementary goods. M = The money income of the consumer. T = The taste or preference of the consumer. A = The advertisement effects. E= Price expectations. U = Unknown variables or influences OTHER DETERMINANTS OF MARKET DEMAND….. Problem: Suppose that the demand for a popular brand of a fruit drink is given by the equation: Qx=10-5Px+0.001I+10Py Where: • Qx= monthly consumption of the fruit per family in gallons. • Px= price per gallon of the fruit drink=2.00birr. • I= median annual family income=20,000birr. • Py= price per gallon of a competing brand of friut drink=2.50birr. Required: a. Interpret the parameter estimates. b. Calculate the monthly consumption of the gallon given the parameters. c. Rewrite the demand function. d. Suppose that a median annual family income increased to 30,000. How does this change the answer to part b. OTHER DETERMINANTS OF MARKET DEMAND….. Solution a. According to our demand equation in Qx, a 1 birr increase in the price of the fruit drink will result in a 5-gallon decline in monthly consumption of fruit drink per family. A 1,000 birr increase in median annual family income will result in a 1-gallon increase in monthly consumption of fruit drink per family. Finally, a 1 birr increase in the price of the competing brand of fruit drink will result in a 10-gallon increase in monthly consumption of the fruit drink per family. In other words, the two brands of fruit drink are substitutes. b. Substituting the stated values into the demand equation yields Qx = 10 - 5(2.00) + 0.001(20, 000) + 10(2.50) = 45 gallons c. Qx = 55 - 5Px d. Qx = 10 - 5(2.00) + 0.001(30,000) + 10(2.50) = 55 gallons THE LAW OF SUPPLY Definition: The law of supply asserts that quantity supplied of a good or service is directly (positively) related to the selling price, ceteris paribus. Symbolically: QS = g(P) Fig. The supply curve where: dQs/dP > 0 THE LAW OF SUPPLY… The upward-sloping supply curve illustrates the positive relationship between the quantity demanded of a good or service and its selling price. The market supply curve shows the various amounts of a good or service that profit-maximizing firms are willing to supply at each price. As with the market demand curve, the market supply curve is also the horizontal summation of the individual firms’ supply curves. The market supply curve establishes a relationship between price and quantity supplied. Changes in the price and the quantity supplied of a good or service are represented diagrammatically as a movement along the supply curve. Changes in supply determinants are illustrated as a shift in the entire supply curve. DETERMINANTS OF MARKET SUPPLY Of course, the market price of a good or service is not the only factor that influences a firm’s decision to alter the quantity supplied of a particular good or service. To get a “feel” for whether a firm will increase or decrease the quantity supplied of a particular good or service (assuming the product’s price is given) in response to a particular supply-side stimulus, let us assume that the firms that make up the supply side of the market are “profit maximizers.” Total profit is defined as: π(Q) =TR(Q) -TC(Q) Where π is total profit, TR is total revenue, and TC is the total cost, which are defined as functions of total output Q. DETERMINANTS OF MARKET SUPPLY… Moreover, total revenue may be expressed as the product of the selling price of the product times the quantity sold i.e TR=PQ Total cost, on the other hand, is assumed to be an increasing function of a firm’s output level, which is a function of the productive resources used in its production. The following Equation expresses total cost as a function of labor and capital inputs: TC=f(L,K) DETERMINANTS OF MARKET SUPPLY… If the firm purchases productive resources in a perfectly competitive factors market, the total cost function might be expressed as: TC =TFC +TVC =TFC+PLL + PKK Where TFC represents total fixed cost (a constant), PL is the price of labor, which is determined exogenously, L the units of labor employed, PK is the rental price of capital, also determined exogenously, and K the units of capital employed. DETERMINANTS OF MARKET SUPPLY… The above explanations try to indicate that as a firm’s output level expands, the costs associated with higher output levels increase. In general, let us say that the change in any factor that causes a firm’s profit to increase will result in a decision to increase the quantity the firm supplies to the market, other things remaining the same. Conversely, any change that causes a decline in profits will result in a decline in quantity supplied, other things remaining the same. We have already seen that an increase in product price, which increases total revenue, will result in an increase in the quantity supplied, or a movement to the right and along the supply function. OTHER SUPPLY DETRMINANTS Table: Impacts on supply arising from changes in factors determining supply QS = f (P, PL , E, R, Ps , Pc , Pe , F) THE MARKET MECHANISM: THE INTERACTION OF DEMAND AND SUPPLY On the curve given left, the market equilibrium price is P*. At that price, the quantity of a good or service that buyers are able and willing to buy is precisely equal to Q*, the amount that firms are willing to supply. At a price below P*, the quantity demanded exceeds the quantity supplied. Fig. Market Equilibrium In this situation, consumers will bid among themselves for the available supply of Q, which will drive up the selling price. Buyers who are unable or unwilling to pay the higher price will drop out of the bidding process. At the higher price, profit-maximizing producers will increase the quantity supplied. As long as the selling price is below P*, excess demand for the product will persist and the bidding process will continue. The bidding process will come to an end when, at the equilibrium price, excess demand is eliminated. In other words, at the equilibrium price, the quantity demanded by buyers is equal to the quantity supplied. THE MARKET MECHANISM: THE INTERACTION OF DEMAND AND SUPPLY Problem : The market demand and supply equations for a product are: Qd=25-3P Qs=10+2P where Q is quantity and P is price. Required: What are the equilibrium price and quantity for this product? CHANGES IN SUPPLY AND DEMAND: THE ANALYSIS OF PRICE DETERMINATION Suppose, for example, that medical research finds that coffee have highly desirable health characteristics, triggering an increase in the public’s preference for coffee. DEMAND SHIFTS Other things remaining constant, this would result in a right-shift in the demand curve for coffee. This results in an increase in the equilibrium price and quantity demanded for coffee. on the other hand if research discovers that coffee exhibited highly undesirable health properties, one could have predicted a reduction in the demand for coffee, or a left-shift in the demand curve, resulting, in turn, in a decline in both equilibrium price and quantity demanded. CHANGES IN SUPPLY AND DEMAND…… SUPPLY SHIFTS Suppose there is a sharp decline in the price of coffee inputs. The result will be an increase in the supply of coffee at every price, other things remaining the same. This, of course, would result in a rightshift of the supply function. The result, which is illustrated in the left figure, is a decline in the equilibrium price and an increase in quantity supplied. Conversely, a left-shift in the supply curve would have raised the equilibrium price and lowered the equilibrium quantity. In either the case of a demand shift or a supply shift, the effect on the equilibrium price and quantity is unambiguous. CHANGES IN SUPPLY AND DEMAND….. DEMAND AND SUPPLY SHIFTS When changes in both demand and supply occur simultaneously, it is more difficult to predict the effect on price and quantity demanded. This can be illustrated by considering four possible cases. Figure C Case 1: An Increase in Demand and an Increase in Supply As illustrated in Figure C a right-shift in both the demand and supply curves yields an ambiguous increase in quantity demanded. The effect on the equilibrium price, however, is indeterminate. CHANGES IN SUPPLY AND DEMAND….. As shown earlier, if the increase in supply is relatively less than the increase in demand, the result will be a net increase in price. This is seen in Figure C by comparing the market clearing price at E with E’. On the other hand, if there occurs a large increase in supply, relative to the increase in demand, the result will be a net decrease in the equilibrium price. This is seen by comparing the market clearing price at E with E” in Figure C. CHANGES IN SUPPLY AND DEMAND….. Case 2: An Increase in Demand and a Decrease in Supply As illustrated in Figure D, a right-shift in the demand curve and a left shift in The supply curve result in an ambiguous increase in the equilibrium price, although the effect on the equilibrium quantity is indeterminate. If the decrease in supply is relatively less than the increase in demand, the result will be an increase in equilibrium price and quantity. Figure D CHANGES IN SUPPLY AND DEMAND….. This is seen in Figure D by comparing the equilibrium price and quantity at E with E’. If, however, the decrease in supply is relatively more than the increase in demand, the result will be an increase in the equilibrium price but a decrease in the equilibrium quantity. This can be seen by comparing the equilibrium price and quantity at E with E”. CHANGES IN SUPPLY AND DEMAND….. Case 3: A Decrease in Demand and a Decrease in Supply As can be seen in Figure E, a left-shift in both the demand and supply curves will result in an unambiguous decline in the equilibrium quantity and an indeterminate change in the equilibrium price. Figure E CHANGES IN SUPPLY AND DEMAND….. If the decrease in supply is relatively less than the decrease in demand, the result will be a decrease in the equilibrium price and quantity. This is seen by comparing equilibrium price and quantity at E with E’ in Figure E. If, however, the decrease in supply is relatively greater than the decrease in demand, the result will be a decrease in the equilibrium quantity, but an increase in the equilibrium price. This can be seen by comparing the equilibrium price and quantity at E with E” in figure E. CHANGES IN SUPPLY AND DEMAND….. Case 4: A Decrease in Demand and an Increase in Supply In our final case, a left-shift in the demand curve and a right-shift in the supply curve will result in an ambiguous decline in the equilibrium price, but an indeterminate change in the equilibrium quantity. This situation is depicted in Figure F. Figure F. CHANGES IN SUPPLY AND DEMAND….. If the increase in supply is relatively less than the decrease in demand, the result will be a decrease in the equilibrium price and quantity. This is seen by comparing the equilibrium price and quantity at E with E” in figure F. If, however, the increase in supply is relatively greater than the decrease in demand, the result will be an increase in the equilibrium quantity and a decrease in the equilibrium price. This can be seen by comparing the equilibrium price and quantity at E’ with E” in Figure F. CHANGES IN SUPPLY AND DEMAND….. Problem : The market supply and demand equations for a given product are given by the expressions: QD = 200 - 50P QS = -40 + 30P a. Determine the equilibrium price and quantity. b. Suppose that there is an increase in demand to QD = 300 50P Suppose further that there is an increase in supply to QS = -20 + 30P, What are the new equilibrium price and quantity? c. Suppose that the increase in supply had been QS = 140 + 30P Given the demand curve in part b, what are the equilibrium price and quantity? d. Diagram your results. CHANGES IN SUPPLY AND DEMAND….. Solution a. Equilibrium is characterized by the condition QD = QS. Substituting, we have 200 - 50P = -40 + 30P, P* = 3 Q* = 200 - 50(3) = -40 + 30(3) = 50 b. Substituting the new demand and supply equations into the equilibrium equations yields 300 - 50P = -20 + 30P, P* = 4, Q* = 300 - 50(4) = -20 + 30(4) = 100 c. 300 - 50P = 140 + 30P, P* = 2, Q* = 300 - 50(2) = 140 + 30(2) = 200 Elasticity of Demand While the law of demand establishes a relationship between price and quantity demanded for a product, it does not tell us exactly as how strong or weak the relationship happens to be. This relation, as already discussed, is inverse baring some rare exceptions. However, a manager needs an exact measure of this relationship for appropriate business decisions. Elasticity of demand is a measure, which comes to the rescue of a manager here. It measures the responsiveness of demand to changes in prices as well as changes in income. A manager can determine almost exactly how the demand for her/his product would change when he changes his price or when her/his rivals alter prices of their products. She/he can also determine how the demand for her/his product would change if incomes of her/his consumers go up or down. Elasticity of demand concept and its measurements are therefore very important tools of managerial decision making. Elasticity of Demand…. In this unit, we will discuss the following kinds of demand elasticity: • Price Elasticity: Elasticity of demand for a commodity with respect to change in its price. • Cross Elasticity: Elasticity of demand for a commodity with respect to change in the price of its substitutes. • Income Elasticity: Elasticity of demand with respect to change in consumer’s income. Elasticity of Demand…. PRICE ELASTICITY OF DEMAND Price elasticity of demand can be calculated using either of the mid point formula or the point elasticity. Consider the figure below with a demand equation of Qd=127-50p Elasticity of Demand…. The Mid-Point Formula It should be clear that the choice of A or B as the starting point can have a significant impact on the calculated value of Ep. One way of overcoming this dilemma is to use the average value of QD and P as the point of reference in calculating the averages. The resulting expression for the price elasticity of demand is referred to as the midpoint formula. Elasticity of Demand…. The derivation of the midpoint formula is: Elasticity of Demand…. Using the data from the foregoing illustration, we find that the price elasticity of demand as we move from point A to point B is: On the other hand, moving from point B to point A yields identically the same result. Elasticity of Demand…. Problem: Suppose that the price and quantity demanded for a good are $5 and 20 units, respectively. Suppose further that the price of the product increases to $20 and the quantity demanded falls to 5 units. Calculate the price elasticity of demand. Elasticity of Demand…. Solution. Since we are given two price–quantity combinations, the price elasticity of demand may be calculated using the midpoint formula: Elasticity of Demand…. POINT-PRICE ELASTICITY OF DEMAND The point-price elasticity of demand is defined as: where dQD/dP is the slope of the demand function at a single point. It is, in fact, the first derivative of the demand function. Elasticity of Demand…. Problem: The demand equation for a product is QD = 50 - 2.25P. Required: Calculate the point-price elasticity of demand if P = 2. Solution Elasticity of Demand…. Problem: Suppose that the demand equation for a product is QD = 100 - 5P. If the price elasticity of demand is -1, what are the corresponding price and quantity demanded? Elasticity of Demand…. Elasticity of Demand…. PRICE ELASTICITY OF DEMAND: SOME DEFINITIONS Now that we are able to calculate the price elasticity of demand at any point along a demand curve, it is useful to introduce some definitions. As indicated earlier, in general we will consider only absolute values of ep, denoted symbolically as |ep|. Since ep may assume any value between zero and negative infinity, then |ep| will lie between zero and infinity. . Elasticity of Demand…. Elasticity of Demand…. In some cases, however, the elasticity remains the same throughout the length of the demand curve. Such demand curves can be placed in the following categories: (i) perfectly inelastic (e = 0); (ii) unitary elastic (e = 1); and (iii) perfectly elastic (e = ∞). These three types of demand curves are illustrated below: Elasticity of Demand…. INCOME ELASTICITY OF DEMAND Perhaps the second most frequently estimated measure of elasticity, after the price elasticity of demand, is the income elasticity of demand, which is defined as where I represents some measure of aggregate consumer income. The income elasticity of demand measures the percentage change in the demand for a good or service given a percentage change in income. From the managerial decision-making perspective, the income elasticity of demand is used to evaluate the sales sensitivity of a good or service to economic fluctuations. Elasticity of Demand…. Commodities for which eI > 0 are referred to as normal goods. Sales of normal goods rise with increases in income, and vice versa. Normal goods may be further classified as either necessities or luxuries. A commodity is classified as a necessity if 0 < eI < 1 The sales of such goods (electricity, rent, food, etc.) are relatively insensitive to economic fluctuations. A commodity is classified as a luxury if eI ≥ 1. Such commodities (jewelry, luxury automobiles, yachts, furs, restaurant meals, etc.) are very sensitive to economic fluctuations. Commodities in which eI < 0 are referred to as inferior goods. Sales of inferior good fall with increases in income, and vice versa. While it is difficult to identify inferior goods at the market level, it is easy to hypothesize the existence of inferior goods for individuals. Elasticity of Demand…. CROSS-PRICE ELASTICITY OF DEMAND Another frequently used elasticity measure is the crossprice elasticity of demand, which is defined as: The cross-price elasticity of demand measures the percentage change in the demand for good X given a percentage change in the price of good Y. The crossprice elasticity of demand is used to evaluate the sales sensitivity of a good or service to changes in the price of a related good or service. Elasticity of Demand…. An interpretation of the cross-price elasticity of demand follows from the sign of the first derivative, since the second term on the righthand side of Equation is always positive. When ey > 0, this indicates that the good in question is a substitute, and when the ey < 0, the good In question is a complement. Elasticity of Demand…. OTHER ELASTICITIES Elasticity is a perfectly general concept. Whenever a functional relationship exists, then an elasticity measure in principle exists. That is, for any function y = f(x1, . . . , xn), there exists an elasticity measure such that e = (dy/dxi) (xi/y), for all i = 1, . . . , n. Elasticity of Demand…. Problem: Rubicon & Styx has estimated the following demand function for its world-famous hot sauce, Sergeant Garcia’s Revenge,. Q = 62 - 2P + 0.2I + 25A where Q is the quantity demanded per month , P is the price per unit, I is an index of consumer income, and A is the company’s advertising expenditures per month . Assume that P = 4, I = 150, and A = 4. Required: a. Calculate the quantity demanded. b. Calculate the price elasticity of demand. According to your calculations, is the demand for this product elastic, inelastic, or unit elastic? What, if anything, can you say about the demand for this product? c. Calculate the income elasticity of demand. Is this product a normal good or an inferior good? Is it a luxury or a necessity? d. Calculate the advertising elasticity of demand. Explain your result. Elasticity of Demand….