Economists Toolkit

ECO 4554-01 Economics of State and Local Government The Microeconomist’s Toolkit Consumer and Producer Surplus Consumer Surplus The vertical distance up to a demand curve at any quantity shows the maximum price consumers are willing to pay for a small (marginal) increase in the quantity of the good, service, or activity. This willingness to pay is a dollar measure of the marginal benefit (or marginal utility or marginal value—they all mean the same thing) of the good. The marginal benefit is different at different quantities. In fact, marginal benefit is a decreasing function of quantity; that is the reason demand curves are negatively-sloped. This is the principle of diminishing marginal benefit or diminishing marginal utility: the more of the thing you already have, the less value you place on additional units of it. The marginal benefit of a good minus its price is the (marginal) consumer surplus. It is the net gain to consumers from having a marginal increase in the good instead of the next best alternative good. Diagrammatically, (marginal) consumer surplus at any quantity is the vertical distance between the demand curve and the price. Marginal consumer surplus is positive for all quantities less than the efficient quantity and negative for all quantities of the good greater than the efficient quantity. Aggregate or total consumer surplus is the difference between consumers’ willingness to pay for all units of the good and their total expenditure on the good. Diagrammatically, aggregate consumer surplus at any quantity is the area between the demand curve and the price from zero up to that quantity. At the efficient quantity, consumer surplus is a triangle. Producer Surplus The vertical distance up to a supply curve at any quantity shows the minimum price sellers are willing to accept for a small (marginal) increase in the quantity of the good, service, or activity. This minimum price equals the marginal cost of the good. The marginal cost is different at different quantities. In fact, marginal cost is typically an increasing function of quantity; the more of the thing you already supply, the greater is the incremental cost to supply additional units of it. The difference between the marginal cost of a good to producers and the price they receive for it is their (marginal) producer surplus. It is the net gain to sellers from using their resources to supply a little more of this good instead of the next best alternative use of their resources. Diagrammatically, (marginal) producer surplus at any quantity is the vertical distance between the price and the supply curve. Marginal producer surplus is positive for quantities less than the efficient quantity and negative for quantities greater than the efficient quantity. Aggregate or total producer surplus is the difference between the total cost of supplying a given quantity and the total revenue. Diagrammatically, aggregate producer surplus at any quantity is the area between the price and the supply curve from zero up to that quantity. At the efficient quantity, producer surplus is a triangle.

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ECO 4554-01: Economics of State and Local Government The Microeconomist’s Toolkit Social Surplus The demand curve shows the marginal benefit of the good to consumers. The supply curve shows the marginal cost of supplying the good. The difference between marginal benefit and marginal cost is the net gain to society, both buyers and sellers, from having a marginal increase in the good instead of using the resources for the next best alternative. This is the social surplus. The social surplus is the sum of consumer surplus and producer surplus. Social surplus is independent of price. It depends only on buyers’ marginal benefit and sellers’ marginal cost. The price determines how much of the social surplus is received by buyers and how much is received by sellers, but the price does not determine the total amount of the social surplus. The social surplus is greatest when buyers’ marginal benefit equals sellers’ marginal cost. At any smaller or larger quantity, the social surplus is less. One interpretation of economic efficiency is maximization of social surplus, which explains why we identify the efficient quantity as the quantity at which marginal social benefit equals marginal social cost (or if there are no externalities, marginal benefit equals marginal cost). Examples 1. At the quantity, 40,000 bushels, and the price, $8 per bushel, which area shows the consumer surplus? Answer: Consumer surplus is the difference between demand and total expenditure, or the blue triangle between the demand curve and the price of $8 and lying between 0 and the quantity 40,000. 2. At the quantity, 40,000 bushels, and the price, $8 per bushel, which area shows the producer surplus? Answer: Producer surplus is the difference between supply and total revenue, or the purple triangle between the price of $8 and the supply curve and lying between 0 and the quantity 40,000. 3. At the quantity, 40,000 bushels, and the price, $8 per bushel, which area shows the social surplus? Answer: Social surplus is the difference between marginal benefit (shown by the demand curve) and marginal cost (shown by the supply curve), or the blue and purple triangles combined. 12

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ECO 4554-01: Economics of State and Local Government The Microeconomist’s Toolkit 4. If the price is $8 and the quantity is 40,000, how much is consumer surplus, producer surplus, and social surplus. Answers: Remember that the formula for the area of a triangle is (0.5*base*height). The base of all three triangles is the quantity, 40,000. The height of the CS triangle is $2. So CS=0.5*40,000*$2=$40,000. The height of the PS triangle is $4. So PS=0.5*40,000*$4=$80,000. The height of the SS triangle is $6. So SS=0.5*40,000*$6=$40,000+$80,000-$120,000. 5. Suppose the price is still $8 but the quantity is 20,000. How much is CS, PS, and SS at $8 and 20,000. Answers: CS is still the area between the demand curve and the price from Q=0 up to Q=20,000. But that area is no longer a triangle; it is a trapezoid. There are at least two ways to calculate this area. The trapezoid is composed of a triangle on top of a rectangle so you can compute the areas of these two figures separately and add them together. Or, you notice that the area of the trapezoid equals the area of the original triangle minus the area of a smaller triangle between Q=20,000 and Q=40,000 so you can calculate it is the difference between the larger and the smaller triangle. There is one problem, however; the diagram doesn’t show the value of the point on the demand curve corresponding to Q=20,000. But since the demand curve is linear, it is easy to extrapolate from the values you do know to find that value (or any other value on the demand curve). It is $9. However you do the calculations, CS=$30,000. In the same way, you can find PS=$60,000 and SS=$90,000. 6. Suppose the price is still $8 but the quantity is 50,000. How much is CS, PS, and SS at $8 and 50,000. Answers: CS is still the area between the demand curve and the price from Q=0 up to Q=50,000. But this area is now composed of two triangles, one extending from Q=0 up to Q=40,000 and the other extending from Q=40,000 up to Q=50,000. Notice that the first triangle is above the price and below the demand curve, but this second triangle is below the price and above the demand curve. For all those quantities up to 40,000,MB (shown by the demand curve) is greater than P, which means the gain to buyers is greater than what they have to pay. So CS for the first 40,000 units is positive. But between 40,000 and 50,000, P>MB, meaning the value of these units to buyers is less than they have to pay. There is a net loss to buyers on these units so their CS is negative. To find CS on all 50,000 units, then, you have to subtract the area of the loss to the right of 40,000 from the area of the gain to the left of 40,000. Again, you have to extrapolate to find the point on the demand curve corresponding to Q=50,000 ($7.50). So CS=$37,500. In the same way, you find PS=$75,000 and SS=$112,500. Elasticity of Demand and Supply Read the discussion of price and income elasticities in Fisher, Chapter 4 Appendix. The price elasticity of demand measures the size of the change in quantity demanded relative to the change in price. It is defined as η = [Percentage change in quantity demanded]/[Percentage change in price] The price elasticity of supply measures the size of the change in quantity supplied relative to the change in price. It is defined as ε = [Percentage change in quantity supplied]/[Percentage change in price] Calculating the Price Elasticity of Demand and the Price Elasticity of Supply If you know the percent change in both quantity and price, you can enter them directly into the definitions to find the coefficient of elasticity. If you do not know the percent changes, then you have to calculate them. There are two formulas for calculating elasticities when you don’t know 3

ECO 4554-01: Economics of State and Local Government The Microeconomist’s Toolkit the percent changes, the arc elasticity formula and the point elasticity formula. The formulas for arc elasticity provide consistent and unambiguous estimates of the elasticities. However, it is often more convenient in application to use a point elasticity formula. Arc elasticity: Calculates the change in quantity as a percent of the average of the original and the new quantity and the change in price as a percent of the average of the original and the new quantity. The formula is η = {ΔQ/[(Q1+Q2)] ÷ [ΔP/(P1+P2)] where ΔQ is the change in the quantity, ΔP is the change in the price, and (Q1+Q2) and (P1+P2) measure the average quantity and the average price. [Note: The averages are actually (Q1 +Q2)/2 and (P1 +P2)/2, but in the arc elasticity formula, the 2 appears in both the numerator and the denominator and therefore cancels]. Point elasticity: Calculates the change in quantity as a percent of the original quantity and the change in price as a percent of the original price. The formula is η = (ΔQ/Q1) ÷ {ΔP/P1) To calculate the price elasticity of demand, use the quantity demanded and the change in quantity demanded in these formulas. To calculate the elasticity of supply, use the quantity supplied and the change in quantity supplied. The “law of demand” says there is an inverse relationship between quantity demanded and price. If price increases, quantity demanded decreases. If price decreases, quantity demanded increases. Demand curves are negatively sloped. Because price and quantity demanded always change in opposite directions, the price elasticity of demand is always a negative number. Therefore, the price elasticity of demand is usually stated as the absolute value of the number calculated by the formula, that is, the negative sign is ignored. But note that when working numerical problems, it is best to retain the negative sign to ensure you get the direction of the result correct. Other Elasticities Other elasticities are calculated in the same way as the price elasticities with appropriate change of variables. For example, the income elasticity of demand is calculated using the same formulas with the quantity demanded in the numerator but with income and the change in income in the denominator. A cross-price elasticity of demand between one good and a substitute good or between one good and a complementary good is calculated by using the same formulas with the quantity demanded of the good in the numerator but with the price of the substitute or complement and the change in price of the substitute or complement in the denominator. When Should You Use the Arc Elasticity Formulas? 1. Both quantities and both prices known: If you know both the original price and quantity and the new price and quantity, you can use the arc elasticity formulas to calculate the elasticity. 2. Both quantities and percentage change in price known: If you know both the original quantity and the new quantity, but you only know the percentage change in price, you can also use the arc elasticity formulas. In this case, you don’t need to compute the percentage change in price; you can just enter it directly into the formula. Note, however, that you no longer have a 2 in the denominator, so you cannot cancel the 2 in the numerator.

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ECO 4554-01: Economics of State and Local Government The Microeconomist’s Toolkit 3. Both prices and percentage change in quantity known: If you know both the original price and the new price, but you only know the percentage change in quantity, you can also use the arc elasticity formulas. You don’t need to compute the percentage change in quantity; you can just enter it directly into the formula. Again, the same caveat about using the formula applies; in this case, because there is no 2 in the numerator, you cannot cancel the 2 in the denominator. These same rules apply to the income elasticity of demand or to any other elasticity. When Should You Use the Point Elasticity Formulas? There are four variables in the point elasticity formulas: the change in quantity, the original quantity, the change in price, and the original price. If you know any three of the four and you have an estimate of the elasticity, you can use the point elasticity formulas to calculate the missing variable. Therefore, the point elasticity formula is particularly helpful when you know the elasticity and want to calculate the change in quantity that results from a change in a price or in income, or when you want to calculate the change in a price or in income that would cause a given change in the quantity. 1. Change in quantity and new quantity unknown: If you know the original quantity, you know or can compute the percentage change in price, and you have an estimate of the elasticity, you can use the point elasticity formula to calculate the percent change in quantity. You can then use the percent change in quantity and the original quantity to find the new quantity. 2. Change in price and new price unknown: If you know the original price, you know or can compute the percentage change in quantity, and you have an estimate of the elasticity, you can use the point elasticity formula to calculate the percent change in price. You can then use the percent change in price and the original price to find the new price. You can use the point formula for income elasticity in the same way to find the effect of a change in income on quantity demanded. You can use the point cross-elasticity formula to find the effect of a change in the price of a substitute or complement. There are many empirical studies that provide estimates of the elasticities of demand and supply for various goods and services. Most principles textbooks give examples. There are also many estimates of the price and income elasticities of demand for publicly-provided goods and services. Fisher, Chapter 4, Table 4-1, displays a range of estimates for the price and income elasticities of demand for various local public services and for selected privately-provided goods and services. You should be familiar with these estimates. Elastic, Inelastic, and Unitary Elastic Demand and Supply Price elasticity: Whichever formula you use, if the elasticity is greater than one in absolute value, it means that the percentage change in quantity is larger than the percentage change in price. The good or service or activity is characterized as being elastic in demand or supply with respect to price. If the elasticity is less than one in absolute value, it means that the percentage change in quantity is smaller than the percentage change in price. The good or service or activity is characterized as being inelastic in demand or supply with respect to price.

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ECO 4554-01: Economics of State and Local Government The Microeconomist’s Toolkit Finally, if the elasticity is exactly one in absolute value, it means that the percentage change in quantity is exactly equal to the percentage change in price. The good or service or activity is characterized as being unitary elastic in demand or supply with respect to price. Income elasticity: Similarly for the income elasticity of demand, if the absolute value of the coefficient of elasticity is greater than one, demand for the good or service or activity is elastic with respect to income. A change in income causes a larger percentage change in demand for the good. If the absolute value of the coefficient of elasticity is less than one, demand is inelastic with respect to income. A change in income causes a change in demand that is smaller, measured in percent, than the change in income. If the absolute value of the coefficient of elasticity is exactly one, demand is unitary elastic with respect to income. The percentage change in demand is exactly equal to the percentage change in income that causes it. If the coefficient is positive, the good is a normal or superior good; demand and income are positively related. If the coefficient is negative, the good is an inferior good; demand and income are inversely related. Cross-elasticity: If the absolute value of the coefficient of elasticity is greater than one, demand for the good or service or activity is elastic with respect to the price of the substitute or complement. The percentage change in demand is larger than the percentage change in price of the substitute or complement. If the absolute value of the coefficient of elasticity is less than one, demand is inelastic with respect to the price of the substitute or complement. The percentage change in demand is smaller than the percentage change in the price of the substitute or complement. If the absolute value of the coefficient of elasticity is exactly one, demand is unitary elastic with respect to the price of the substitute or complement. The percentage change in demand is exactly equal to the percentage change in the price of the substitute or complement. If the coefficient is positive, the two goods are substitutes; the quantity of one moves in the opposite direction to the quantity (but the same direction as the price) of the other good. If the coefficient is negative, the two goods are substitutes; the quantity of one moves in the same direction as the quantity (but the opposite direction to the price) of the other good. Examples 1. a. Using the data for wheat from the examples in the section on consumer and producer surplus, calculate the price elasticity of demand for wheat between $8 and $9 using the arc elasticity formula. η = {ΔQ/(Q1+Q2)] ÷ [ΔP/(P1+P2)] = [(40,000-20,000)/(40,000+20,000)] ÷ [(8-9)/(8+9)] = [(20,000)/(60,000)] ÷ [(-1)/(17)] = [.333] ÷ [-.059]

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ECO 4554-01: Economics of State and Local Government The Microeconomist’s Toolkit = -5.64 = 5.64 b. Is the demand for wheat over this range of prices and quantities, elastic, inelastic, or unit elastic? Answer: The absolute value of the coefficient of elasticity, 5.64, is greater than one. Therefore, the percent change in quantity demanded is greater than the percent change in price, and demand is elastic. 2. a. Calculate the price elasticity of supply for wheat between $8 and $9 using the arc elasticity formula. ε = {ΔQ/(Q1 +Q2)] ÷ [ΔP/(P1+P2)] = [(40,000-50,000)/(40,000+50,000)] ÷ [(8-9)/(8+9)] = [(-10)/(90,000)] ÷ [(-1)/(17)] = [-.111] ÷ [-.059] = 1.88 b. Is the supply of wheat over this range of prices and quantities, elastic, inelastic, or unit elastic? Answer: The absolute value of the coefficient of elasticity, 1.88, is greater than one. Therefore, the percent change in quantity supplied is greater than the percent change in price, and demand is elastic. 3. Suppose the current price of wheat is $8 per bushel, the quantity demanded is 40,000 bushels, and the price elasticity of demand is 4.00. Use the point elasticity formula to calculate the decrease in quantity demanded if price increases by $1.00. [Note: To ensure we get the direction of the change correct, it is best to use the negative sign in the calculations.] η = (ΔQ/Q1) ÷ (ΔP/P1) -4.00 = (ΔQ/Q1) ÷ (1/8) (ΔQ/Q1) = -4.00 * (1/8) (ΔQ/Q1) = -4.00 * 0.125 (ΔQ/Q1) = -0.50 (ΔQ/40,000) = -0.50 ΔQ = -0.50 * 40,000 ΔQ = -20,000 Q2 = Q1 + ΔQ Q2 = 40,000 – 20,000 = 20,000

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ECO 4554-01: Economics of State and Local Government The Microeconomist’s Toolkit So a $1.00 or 12.5% increase in the price results in a 50% decrease in quantity from 40,000 bushels to 20,000 bushels. 4. Suppose the current price of wheat is $8 per bushel, the quantity demanded is 40,000 bushels, and the income elasticity of demand is 0.75. Use the point elasticity formula to calculate the increase in quantity demanded of wheat if consumer incomes increase by 25 percent, ceteris paribus. ηI = (ΔQ/Q1) ÷ (ΔI/I1) 0.75 = (ΔQ/Q1) ÷ 0.25 (ΔQ/ Q1) = 0.75 * 0.25 (ΔQ/Q1) = 0.1875 (ΔQ/40,000) = 0.1875 ΔQ = 0.1875 * 40,000 ΔQ = 7,500 bushels Q2 = Q1 + ΔQ Q2 = 40,000 + 7,500 = 47,500 bushels So, a 25% increase in consumer incomes results in an increase in quantity demanded of 18.75% or 7,500 bushels. The ceteris paribus condition is important here. If the price were unchanged at $8 per bushel, quantity demanded would increase by 7,500 bushels when income increased by 25 percent. The demand curve would shift horizontally by a distance equal to 7,500. Of course, after the demand shift, $8 would no longer be an equilibrium price. Instead, with greater demand for wheat, the equilibrium price would increase and the new equilibrium quantity would lie somewhere between the original 40,000 bushels and the 47,500 bushels calculated above under the assumption of no change in price. [Question: If you can, find the new equilibrium quantity and price. If you cannot, explain how you would go about finding the new equilibrium quantity and price.]

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