# Evaluating Policy Interventions. Willingness to Pay and Demand. Consumer Surplus (CS) Market Basics - Econ of NA - RIT - Dr.

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1 Evaluating Policy Interventions Market Basics - Econ of NA - RIT - Dr. Jeffrey Burnette In economics we like to measure the impact government policies have on the economy and separate winners and losers. This way we can properly assess the effectiveness of the policy and determine whether it is having its intended result. Marginal Benefit - the extra happiness that a person receives from consuming one more unit of a good or service. Marginal Cost - the additional cost (including opportunity cost) of producing one more unit of a good or service. Willingness to Pay and Demand Since we derived the demand curve by asking the question: If the price of the product is \$x how many units would you like to buy? Therefore, the demand curve is the maximum amount that an individual is willing to pay for the last unit of a good or service consumed. The maximum amount they are willing to pay for a particular unit is equal to the marginal benefit they receive from consuming that unit. Consumer Surplus (CS) Since people are not forced to pay the maximum price they are willing to pay for each unit, they receive a consumer surplus. The value of a good minus the price paid for each unit consumed. Consuming Infinitely Divisible Units Vs. Whole/Partial Units Products are sold in either infinitely divisible units or whole units only. Products like gasoline can be purchased in the exact amount you would like; these are infinitely divisible. Other products can only be purchased in specific increments. It s not possible to purchase half a bottle of soda or half of a slice of pizza. 1

2 Consumer Surplus with Whole Units CS n = n (MB i P ) i=1 Assume Q D = 10 - P and the P = \$7 If the price of the product is \$7 then the consumer will buy 3 units. The individual is willing to pay \$9 for the first unit, \$8 for the second unit and \$7 for the third unit. However she pays only \$5 for each unit. Therefore, the consumer surplus will be CS 3 = 3 i=1 (MB i P ) = (9-7) + (8-7) + (7-7) = \$3. Consumer Surplus with Infinitely Divisible Units If however, the individual can consume infinitely divisible units then we calculate the Consumer Surplus as the area of the triangle between the demand curve and the price paid for the product. Often times this is a triangle or trapezoid but this is not always the case. 2

3 Producer Surplus (PS) Since firms are not forced to receive the minimum price for which they are willing to sell each unit, they receive a producer surplus. The producer surplus is the price of the good received minus the minimum supply price for each unit consumed. Producer Surplus with Whole Units P S n = n (P MC i ) i=1 Assume Q s = P and the P = \$3 If the price of the product is \$3 then the firm will sell 3 units. The firm is willing to sell the first unit for \$1, the second unit for \$2 and the third unit for \$3. However it receives \$3 for each unit. Therefore, the producer surplus will be P S 3 = 3 i=1 (P MC i) = (3-1) + (3-2) + (3-3) = \$3. 3

4 Producer Surplus with Infinitely Divisible Units If however, the firm can sell infinitely divisible units then we calculate the Producer Surplus as the area of the triangle between the supply curve and the price received for the product. Social Welfare 1 (SW) - The aggregate benefit to society due to the existence of a good or service. In the previous cases there are only two types of actors in the market consumers and firms therefore Social Welfare is given by the following equation, SW = CS + PS. In later cases government will levy a tax or provide a subsidy changing the Social Welfare to the following equation, SW = CS + PS + TAX or SW = CS + PS - SUB. 1 Note: When determining the social welfare for a particular market you need to remember to include all participants in the market and measure the amount of happiness they receive because the market exists. 4

5 Underproduction When the market produces a quantity less than the equilibrium quantity then the MSB>MSC. Conceivably, we could pay firms a lump-sum to increase production. Overproduction When the market produces a quantity greater than the equilibrium quantity then the MSC>MSB. If firms produce a lower quantity than equilibrium then a social planner could make society better off by reducing the quantity produced. Deadweight Loss - the decrease in social welfare that results from producing an inefficient quantity. The Minimum Wage The minimum wage is a price floor is imposed by the government. When binding, it forces firms to pay a higher wage than what would have been determined in equilibrium. Since firms are forced to pay a higher wage there is a decrease in the quantity of labor demanded. Likewise, this higher wage induces individuals to increase their quantity of labor supplied, creating an excess supply (or surplus) of labor and causes unemployment. Under normal circumstances the wage would lower to achieve equilibrium, but due to governmental policy this is prevented. Instead, firms decide to decrease the quantity of labor demanded leaving a number of those who had jobs unemployed. In addition, since the number of people looking for a job has increased and the number of available jobs has decreased it will be even more difficult to move from being unemployed to employed. Fair Labor Standards Act of 1938 Established federal minimum wage at \$0.25 an hour. Increased or expanded coverage to additional workers 29 times. Last change effective July 24, 2009 raised the minimum wage from \$6.55 to \$7.25 an hour. Each state may set its minimum wage higher than the federal minimum. Currently the minimum wage in New York State is \$8 per hour. It will increase to \$8.75 per hour starting January 1, 2014 and to \$9.00 per hour starting January 1,

6 Taxes In the previous discussion of equilibrium the price paid by consumers to purchase a product was equal to the price received by firms. When taxes are imposed the price paid by the individual consumer (P P ) is greater than that received by the selling firm (P R ). The relationship between the price paid and that received is: where T is the per unit tax levied on consumers. P P = P R + T (1) If the government imposes a per unit tax on firms the relationship is: P R = P P T (2) Government Imposes a Tax on Consumers If government levies a per unit tax on consumers then we need to substitute Equation (1) into the demand equation and then solve for equilibrium. To illustrate this we will use the following information: 6

7 10 P P = P R (4) Market Basics - Econ of NA - RIT - Dr. Jeffrey Burnette Q D = 10 P P Q S = P R T = 2 (3) From before we know that the equilibrium price is \$5 and that the equilibrium quantity is 5 units. Setting supply and demand equal results in: Q D = Q s At this point we have 1 equation and 2 unknowns (P P, P R ). This is where we need the information on taxes. Since, the tax is imposed on the buyer we use Equation (1). 10 (P R + 2) = P R 10 P R 2 = P R 8 = 2P R P R = 4 Now that we know the price that sellers receive we can plug this into the supply equation to calculate the equilibrium level of output. (Q T = 4) We can also find out the price purchasers pay. (P P = P R + 2 = 6) Revenue raised from the tax is equal to T Q T. (TR = \$8) 7

8 Government Imposes a Tax on Firms When government enacts a per unit tax to be paid by firms we have to modify the supply function by substituting Equation (2) into the supply equation. This is just like what we did when calculating equilibrium with a tax on buyers. Using the same information we now impose a \$2 tax on firms. 10 P P = P R 10 P P = (P P 2) 12 P P = P P 12 = 2P P P P = 6 Now that we know the price that consumers pay we can plug this into the demand equation to calculate the equilibrium level of output. (Q T = 4) We can also calculate the price firms receive. (P R = P P - 2 = 4) Revenue raised from the tax is equal to T Q T. (TR = \$8) You should notice that it makes no difference if the tax is imposed on consumers or firms. Consumers end up paying \$6 and firms end up receiving \$4 with an equilibrium quantity of 4 units. Furthermore, in this instance consumers and firms end up dividing the tax equally. Consumers used to pay \$5 for the product and are now forced to pay \$6. So, they are paying \$1 more for the same product and therefore \$1 of the \$2 tax. Firms used to receive \$5 for their product but now they only get \$4. So, they also pay \$1 of the \$2 tax. In general, the largest tax burden is borne by the group that is less sensitive to price changes, the elasticity of demand relative to that of supply. In this example the slope of the demand curve (-1) is the same magnitude as that of the supply curve (1). This is why the tax is 8

9 divided equally. 2 If the slope of the supply curve were greater than 1 in magnitude then consumers would bear a larger portion of the tax. Social Welfare and Taxes Earlier we analyzed the social benefit due to the existence of a market. Social benefit was initially separated into consumer and producer surplus. In the diagram above, the consumer surplus is the area of the upper left triangle (\$12.50) while the producer surplus is the area of the lower left triangle (\$12.50). Social welfare is the sum of all participants in the market (\$ \$12.50 = \$25) The addition of taxes causes each consumer to pay a higher price for the same product and purchase fewer units. This means that the consumer surplus has decreased. (The new consumer surplus is now \$8) Likewise, the producer surplus decreases because firms receive a lower price for their product and sell fewer units. (The new producer surplus is now \$8.) This reduction in consumer and producer surplus is illustrated in the graph below. 2 While it s true that slope and elasticity are different measurements and we generally can t compare them it is possible in this instance because the units on both the x and y axis are exactly the same. 9

10 The imposition of a tax causes a new participant to gain from the market s existence, government is going to generate tax revenue. (The amount of tax revenue generated is \$8) When tax revenue is added to the new consumer surplus and producer surplus the total benefit to society is now \$24. This is \$1 less than the social welfare without the tax, so society is worse off because of this policy. The lost \$1 of social welfare is called the deadweight loss, and is illustrated in the above diagram by the 2 very small triangles just to the left of the intersection of the supply and demand curves. Subsidies In the previous discussion, taxes were imposed and the price paid by the individual consumer (P P ) is greater than that received by the selling firm (P R ). In the case of a subsidy we get the opposite relationship, the price received by the firm is greater than the price paid by the consumer. The relationship between the price paid and that received is: where S is the per unit subsidy given to firms. P R = P P + S (5) If the government gives a per unit subsidy to consumers the relationship is: P P = P R S (6) 10

11 Government Gives a Subsidy to Firms When government gives a per unit subsidy to firms we have to modify the supply function by substituting Equation (5) into the supply equation. This is just like what we did when calculating equilibrium with a tax. Using the same information as the tax example we now give a \$2 subsidy to firms. 10 P P = P R 10 P P = (P P + 2) 8 P P = P P 8 = 2P P P P = 4 Now that we know the price that consumers pay, we can plug this into the demand equation to calculate the equilibrium level of output. (Q S = 6) We can also find out the price firms receive. (P R = = 6) The total amount of the subsidy given is equal to S Q S. (Total subsidy = \$12) You should notice that a subsidy has the opposite effect as a tax on quantity produced. However, like taxes where the burden was split, the benefit of a subsidy is also divided up between firms and consumers based upon the relative elasticities of supply and demand. Here consumers used to pay \$5 for the product and now only pay \$4. So, they are receiving \$1 of the \$2 subsidy. Firms used to receive \$5 for their product but now receive \$6. So, they are getting \$1 of the \$2 subsidy. 11

12 Social Welfare and Subsidies A subsidy causes each consumer to pay a lower price for the same product and therefore she purchases more units. This means that the consumer surplus increases. (The new consumer surplus is now \$18) Likewise, the producer surplus increases because they receive a higher price for their product and sell more units. (The new producer surplus is now \$18.) Initially it might appear that society is better off and should therefore subsidize every product however remember the government had to spend money increase production. When the amount of the subsidy is subtracted from the sum of the new consumer surplus and producer surplus the total benefit to society is now \$24. (\$18 + \$18 - \$12 = \$24) This is \$1 less than the social welfare without the tax, so society is also worse off by this policy. The deadweight loss is again \$1 and is illustrated in the above diagram by the 2 small triangles just to the right of the intersection of the supply and demand curves. 12

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