layout: true background-image: url(figs/tcb-logo.png) background-position: bottom right background-attachment: fixed; background-origin: content-box; background-size: 10% --- class: title-slide .row[ .col-7[ .title[ # Principles of Macroeconomics ] .subtitle[Public Goods and Common Pool Resources] .author[ ### Dennis A.V. Dittrich ] .affiliation[ ] ] .col-5[ ] ] --- class: practice-slide # 1. .col-8[ When is a good non-excludable? Give one example. When is a good nonrival in consumption? Give one example. ] --- # Taxonomy of Goods .row[ .col-6[ ### Samuelson's Classification * One person's consumption substracts from the total available to others. * One person's consumption **does not** substract from the total available to others. ] .col-6[ ### Musgrave's Classification * Exclusion is feasible. * Exclusion is **not** feasible. ]] ||Rivalry in Consumption|No Rivalry in Consumption| |---|:---:|:---:| |Exclusion is Feasible|Private Good|**Club Good**| |Exclusion is Not Feasible|**Common Pool Resource**|**Public Good**| | <td colspan=2 style="text-align:center;"> **Common Goods** | --- class: practice-slide ## 2. .col-8[ Some media companies run ads claiming that downloading or copying media is the same thing as stealing a DVD from a store. Let’s see if this is the case. a. Is a DVD a nonrival good? Why or why not? b. Suppose someone stole a DVD from a retail outlet. Regardless of how that person values the DVD, does the movie company lose any revenue as a result of the theft? Why or why not? ] ??? a. The DVD is a rival good because one person owning a DVD means another person cannot own that DVD. b. They lose revenue because someone could have bought that DVD. --- class: practice-slide ## 2. .col-8[ c. Suppose someone illegally downloaded a movie instead of purchasing it. Also suppose that person placed a high value on the movie (they valued it more than the price required to purchase it legally). Does the movie company lose any revenue as a result of the theft? Why or why not? d. Suppose someone illegally downloaded a movie instead of purchasing it. Also suppose that person placed a low value on the movie (they valued it less than the price required to purchase it legally). Does the movie company lose any revenue as a result of the theft? Why or why not? e. How is illegally downloading media like retail theft and how is it not? ] ??? c. They lose revenue because if that person did not download the movie, he would have bought the DVD. d. They did not lose revenue because if that person did not download the movie, he wouldn’t have bought the DVD, anyway. e. When you value the movie more than the price, downloading it is like stealing because you are denying the company your patronage. If you value the movie less than the price, you will never buy the movie, so downloading it does not make the company worse off but it increases your utility. Thus, stealing DVDs is not quite the same as downloading. In the first case, the thief ’s gain always comes at the expense of the producer. In the second case, the thief can gain without the producer losing. ??? ## When Should a Public Good be Provided? .row[ .col-6[ A two-person flat share is considering buying a TV. The unit would be in the common room. The budget constraints of the two flat share members are: `\begin{align*} x_1+g_1&=w_1\\ x_2+g_2&=w_2 \end{align*}` `\(w_i\)` : initial assets of `\(i\)` `\(x_i\)` : money for private consumption `\(g_i\)` : contribution to the public good TV ] .col-6[ The TV set costs `\(c\)`. If `\begin{align*} g_1+g_2&\geq c \end{align*}` The device can be purchased. The utility functions of the flat share members are: `\begin{align*} u_1(x_1,G)\\ u_2(x_2,G) \end{align*}` The maximum willingness to pay (the reservation price) `\(r_i\)` that makes consumers indifferent `\begin{align*} u_1(x_1-r_1,1)&=u_1(x_1,0)\\ u_2(x_2-r_2,1)&=u_2(x_2,0) \end{align*}` ]] ??? # Provision of a Public Good .row[ .col-7[ Acquiring the TV leads to a Pareto improvement: `\begin{align*} u_1(w_1,0)&< u_1(x_1,1) &\text{ mit } x_1&=w_1-g_1\\ u_2(w_2,0)&< u_2(x_2,1) &\text{ mit } x_2&=w_2-g_2\\ \end{align*}` Using `\(r_i\)` follows: `\begin{align*} u_1(w_1-r_1,1)=u_1(w_1,0)< u_1(x_1,1) =u_1(w_1-g_1,1)\\ u_2(w_2-r_2,1)=u_2(w_2,0)< u_2(x_2,1) =u_2(w_2-g_2,1) \end{align*}` `\begin{align*} u_1(w_1-r_1,1)< u_1(w_1-g_1,1)\\ u_2(w_2-r_2,1)< u_2(w_2-g_2,1) \end{align*}` ] .col-5[ `\begin{align*} r_1> g_1, &&r_2> g_2 \end{align*}` The maximum willingness to pay is higher than the amount to be paid, meeting the necessary conditions for the existence of a Pareto improvement. The sum of the willingness to pay is larger than the cost. `\begin{align*} r_1+r_2>g_1+g_2=c \end{align*}` Also the sufficient condition for the existence of a Pareto improvement is met. At least one payment plan `\((g_1,g_2)\)` can be found in order to satisfy the necessary condition that every consumer will be better off buying the good. ] ] ??? # Provision of a Public Good .col-7[ `\begin{align*} c&>r_i\\ r_1+r_2&>c\\ r_1+r_2&>g_1+g_2=c \end{align*}` The under-production of public goods is analogous to the over-production of goods that generate negative externalities. ] .large[ |||Player B|| |---|---|:---:|:---:| ||| Buys| Doesn't buy| |**Player A**|Buys| `\(u_1(w_1-g_1,1),\)` | `\(u_1(w_1-c,1),\)` | ||| `\(u_2(w_2-g_2,1)\)` | `\(u_2(w_2,1)\)` | ||Doesn't buy| `\(u_1(w_1,1),\)` | `\(\bf{u_1(w_1,0),}\)` | ||| `\(u_2(w_2-c,1)\)` | `\(\bf{u_2(w_2,0)}\)` | ] --- class: practice-slide # 3. .col-8[ What are free riders? ] --- # Public Goods and Free Riding .col-7[ * Occurs because there is no possibility to provide the service without benefiting everyone. * As a result, households have no incentive to pay what the pubic good really is worth to them. * Free-riders understate the value of the good so that they can enjoy the benefit of the good without paying for it. * With public goods, the presence of free riders makes it difficult or impossible for markets to provide goods efficiently because of their non-exclusion characteristic. ] --- class: practice-slide .row[.col-8[ # 4. The economic theory of public goods makes a very clear prediction: If the benefits of some action go to strangers, not to yourself, then you won’t do that action. Economists have run dozens of experiments testing out this prediction. A typical “public goods game” is quite simple: Everyone in the experiment is given, say, $5 each, theirs to take home if they like. They’re told that if they donate money to the common pool, all the money in the pool will then be doubled. The money in the pool will then be divided equally among all players, whether they contributed to the pool or not. That’s the whole game. Let’s see what a purely self-interested person would do in this setting. ] .col-4[ a. If 10 people are playing the game, and they all chip in their $5 to the pool, how much will be in the pool after it doubles? b. So how much money does each person get to take home if everyone puts the money into the pool? ] ] ??? a. $100: 10 x $5 x 2. b. $10: $100/10. --- class: practice-slide # 4. .col-8[ c. Now, suppose that you are one of the players, and you’ve seen that all 9 other players have put in all their money. If you keep your $5, and the pool money gets divided up equally among all 10 of you, how much will you have in total? d. So are you better or worse off if you keep your money? e. What if none of the nine had put money into the pot: If you were the only one to put your money in, how much would you have afterward? Is this better or worse than if you’d just kept the money yourself? ] ??? c. There will be $90 in the pool, so your share of the pool is $9. You get that $9, plus your own $5. That means you get to keep $14 total. Compare with your answer to part b. d. You are better off if you keep your money. e. If you were the only one to put money in, your $5 would turn into $10, which would be divided up among all 10 players. You’d get to take home just $1. That’s clearly worse than keeping the original $5 all for yourself. --- class: practice-slide # 4. .col-8[ f. So if you were a purely self-interested individual, what’s the best thing to do regardless of what the other players are doing: Put all the money in, put some of it in, or put none of it in? (Answer in percent.) Do the benefits of donating go to you or to other people? g. If people just cared about “the group,” they’d surely donate 100%. In part f, you just said what a purely self-interested person would do. In the dozens of studies that Ostrom summarizes, people give an average of 30% to the common pool. So, are the people in these studies closer to the pure self-interest model from part f, or are they closer to the pure altruist model of human behavior? ] ??? f. In both the case in which nine players gave and the case in which nobody but you gave, the best option was to keep your money for yourself—put nothing into the common pool. In fact, no matter what anyone else does the best thing for you to do is to opt out: To keep all $5 for yourself, and just hope that other players are foolish enough or altruistic enough to donate their money. You should donate 0 percent. The benefits of donating go to other people. g. People are closer to the pure-self-interest model: 30% is closer to 0% than it is to 100%. Ostrom, a political scientist, won the 2009 Nobel Prize in Economics for her work in discovering which real-world institutions encourage solutions to public goods problems. Her widely-read book Governing the Commons is highly recommended. --- # How Much of the Public Good? .row[.col-7[ Two neighboring merchants consider whether and how many guards should they hire. ![](img13/pub_good1.png) ] .col-5[ * At a wage of 10 merchant 1 hires four guards * Merchant 2 does not hire any guards * Pareto-Optimum would be five guards. The social demand or willingness to pay for a public good is the **vertical** sum of the individual demand curves. ]] --- # Efficient Provision of a Public Good .col-7[ * If a good in non-rival, the social utility of consumption is determined by the vertical summation of the individual demand curves for the good. * For goods with rival consumption individual demand curves of the good are added horizontally. ] --- class: practice-slide # 5. .col-8[ a. Has the rise of the Internet and file sharing turned media such as movies and music into public goods? Why? b. Taking your answer in part a into account, would government taxation and funding of music improve social welfare? In your answer, at least mention some of the practical difficulties of doing this. ] ??? a. Movies and music are nonrivalrous but they used to be excludable, making them nonrival private goods. Today, however, the ease of copying makes digital movies and music nonexcludable. (Although certain technologies may discourage free riding by some, especially older users who can’t figure out how to copy, they are still nonexcludable to many people.) That makes movies and music transform into public goods for a large portion of the population. b. Government funding of music would be a classic way to solve a public goods problem, but the government would face the difficult problem of figuring out whom to fund. Would government-funded music be boring and committee-driven? Would the government ever have funded the Rolling Stones? Or would it be too fancy for most listeners to enjoy? Or would it strike a good middle ground of pushing the boundaries of music, without wasting taxpayer money on music that only five people like? Perhaps the government can just subsidize music education (e.g., pay for more music schools) and leave most decisions in private hands. Of course, most governments, including the United States, already spend money encouraging the production of music skills and music production: So, we would have to check and see if the current amount of government subsidy is above, equal to, or below the optimal level already. ??? # How Much of the Public Good? .col-7[ The welfare function is: `$$W=\sum_i \alpha_i U_i(x_i,G) \text{ mit } \alpha_i>0$$` The maximization problem for the society is then `\begin{align*} \max_{x_i,G,t_i} \sum_i \alpha_i U_i(x_i,G) &\text{ s.t.}\\ \text{Budget constraint}\\ I_i=x_i+t_i\\ \text{Expenditure public good}\\ \sum_i t_i=pG \end{align*}` ] ??? # How Much of the Public Good? .row[ .col-7[ `\begin{align*} \mathcal{L} =\sum_i \alpha_i U_i(x_i,G) -\lambda(\sum_i t_i-pG) -\sum_i \mu_i(I_i-x_i-t_i) \end{align*}` ]] .row[.col-6[ First order conditions: `\begin{align} \frac{\partial \mathcal{L}}{\partial x_i} &= \alpha_i\frac{\partial U_i}{\partial x_i} + \mu_i = 0\tag{1}\\ \frac{\partial \mathcal{L}}{\partial G} &= \sum_i \alpha_i \frac{\partial U_i}{\partial G} +\lambda p =0\tag{2}\\ \frac{\partial \mathcal{L}}{\partial t_i} &= -\lambda +\mu_i = 0 \quad\Rightarrow \lambda = \mu_i\tag{3} \end{align}` `\begin{align} \text{From (1) and (3) follows: }\alpha_i =\frac{-\lambda}{\dfrac{\partial U_i}{\partial x_i}} \end{align}` ] .col-6[ Plugging `\(\alpha\)` in equation (2) gives: `\begin{align} \sum_i \frac{-\lambda}{\dfrac{\partial U_i}{\partial x_i}} \frac{\partial U_i}{\partial G} +\lambda p &=0\\ -\lambda\sum_i \frac{\dfrac{\partial U_i}{\partial G}}{\dfrac{\partial U_i}{\partial x_i}} - p &=0\\ \sum_i \frac{\dfrac{\partial U_i}{\partial G}}{\dfrac{\partial U_i}{\partial x_i}}&=p \end{align}` ] ] ??? # How Much of the Public Good? .col-7[ * `\(\dfrac{\dfrac{\partial U_i}{\partial G}}{\dfrac{\partial U_i}{\partial x_i}}\)` is the marginal rate of substitution between private consumption and the public good. * The marginal rate of substitution between private consumption and public good can be interpreted as the **marginal willingness to pay** for an additional unit of the public good. * In the Pareto-Optimum the sum of the individual marginal willingness to pay for the public good equals the marginal cost of the public good. ] ??? # Private Provision --- Nash-Equilibrium .row[ .col-6[ Utility `$$U_i=U_i(X_i,G)$$` Provision `$$G=g_1+g_2$$` Budget constraint `$$I_i=X_i+g_i \quad (p_G=1=p_X)$$` Maximization problem `$$max_{g_i}U_i=U_i(I_i-g_i,g_1+g_2)$$` ] .col-6[ Reaction function -- individual demand for the public good `\begin{align*} -\frac{\partial U_i}{\partial X} +\frac{\partial U_i}{\partial G}&=0\\ \frac{\dfrac{\partial U_i}{\partial G}}{\dfrac{\partial U_i}{\partial X}}&=1 \quad \left(=\frac{p_G}{p_X}\right)\\ g_1&=g_1(g_2,I_1)\\ g_2&=g_2(g_1,I_2)\\ g_i&\in [0,I_i/p_G] \end{align*}` ] ] ??? ## Private Provision --- Nash-equilibrium --- Example .row[ .col-6[ Utility `$$U_i= X_iG$$` Budget constraint `$$10=X_i+g_i \quad (p_G=1=p_X)$$` Maximization problem `$$max_{g_i}U_i=(10-g_i)\times(g_1+g_2)$$` ] .col-6[ Reaction function -- individual demand for the public good `\begin{align*} \frac{\partial U_i}{\partial g_i}&= -(g_1+g_2)+(10-g_1)=0\\ \Rightarrow 2g_1 &= 10-g_2\\ g_1&=\frac{10-g_2}{2}\\ g_2&=\frac{10-g_1}{2} \end{align*}` * Equilibrium `\begin{align*} g_1=g_2=\frac{10}{3} \end{align*}` ] ] ??? ## Private Provision --- Nash equilibrium --- Example .col-7[ Is the Nash equilibrium efficient? Pareto-Optimum `\begin{align*} \sum_i MRS^{G,X} &= MRT^{G,X}\\ \frac{10-g_1}{g_1+g_2}+\frac{10-g_2}{g_1+g_2}&=1\\ g_1+g_2&= G = 10 \end{align*}` Nash Equilibrium `\begin{align*} g_1&=g_2=\frac{10}{3}\\ G&=\frac{20}{3} && (G_{Pareto}=10)\\ U_i\left(\frac{20}{3},\frac{20}{3}\right)&=\frac{20}{3}\times \frac{20}{3} = \frac{400}{9} && \left(U_i(5,10)=\frac{450}{9}\right) \end{align*}` ] --- # Private Preferences for Public Goods .col-7[ * Government production of a public good is advantageous because the government can collect taxes or fees to pay for it. * Still, the government needs to determine how much of a public good to provide when the free rider problem gives people an incentive to misrepresent their preferences. ] --- # Voting and Public Goods .row[ .col-7[ Voting for putting up a new traffic light The cost of the traffic light is 300. The government finances the traffic light by a lump sum tax, i.e. everyone has to pay an equal share. ||Willingness to pay|||Total value to|| |---|---|---|---|---|---| |Location | Huey | Dewey | Louie | Society | Result | |Intersection A | 50 | 100 | 150 | 300 |Yes | |Intersection B | 50 | 75 | 250 | 375 | No| |Intersection C | 50 | 100 | 110 | 260 | Yes | The majority vote is inefficient since the preference of every citizen is equally weighted. ] .col-5[ There is an efficient outcome, which is the weighted vote of every citizen according to the strength of their preference. Unfortunately each citizen has an incentive to lie... #### Incentive Compatible Mechanism for Preference Elicitation There is a mechanism that leads to truthful disclosure of individual preferences: The Groves-Clark-Mechanism * Pivotal citizens have to pay an extra tax depending on the strength of their revealed preference for the public good. * This mechanism can be gamed by coalitions of citizens. * It does not guarantee that enough taxes are collected to finance the optimal level of the public good; it may also generate excess tax revenues. ]] --- # Summary .col-7[ * Goods that private markets are not likely to produce efficiently are either nonrival and nonexclusive. Public goods are both. * Characteristics of public goods: * Nonrival: for any given level of production, the marginal cost of providing it to an additional consumer is zero. * Nonexclusive: it is expensive or impossible to exclude people from consuming it. * A public good is provided efficiently when the vertical sum of the individual demands for the good is equal to the marginal cost of producing it. * Majority-rule voting is one way for citizens to voice their preference for public goods: this does not necessarily lead to the efficient outcome. ] --- class: practice-slide # 6. .row[ .col-5[ ![](img13/milk.jpg) ] .col-7[ Two girls are sharing a cold chocolate milk, as in the picture. How long do you think it will take them to drink all the milk? How long would it take if each girl had their own glass and half the milk? Can you see a problem when the girls drink from a common glass? ] ] ??? They’ll drink quite quickly if they are drinking out of just one glass. They’d drink more slowly and more enjoyably if they each had “private property” over half the milk. --- # Common Property Resources .row[ .col-5[ * Everyone has free access to these resources. * Consequently, there is often an overuse. * Examples * Air and water * Fish and livestock ] .col-7[ ![](img13/c18-01.png) ]] --- class: practice-slide # 7. .col-8[ Chickens and the “chicken of the sea” (tuna) are fundamentally different in terms of population though they are both food. Indeed, chickens are eaten far more than tuna, and chickens are abundant compared with their ocean-living cousins. a. What difference between these two species does this chapter identify as the explanation for this seemingly strange puzzle? b. As population and prosperity has increased, the demand for chicken has increased. What happens to the price of chickens as a result? Why? ] ??? a. Chickens are an owned resource; tuna is not. b. The price of chicken goes up as more people bid for the same number of chickens (all other things being equal). --- class: practice-slide # 7. .col-8[ c. Because of the rules humans have concerning chickens, what happens to the number of people raising chickens as a result of the price change? Why? What happens to the number of chickens? Why? d. What happens to the price of tuna as population and prosperity increase? Why? e. Because of the rules humans have concerning tuna, what happens to the number of people harvesting tuna as a result of the price change? Why? ] ??? c. The increased price encourages more people to raise chickens; the number of chickens increases. d. The price increases because more people bid for the same number of tuna. e. More people harvest tuna to take advantage of the higher price. But because they are not encouraging more tuna to be born and raised, the total amount of tuna falls. ??? ## Common Property Resources -- An Example .row[ .col-6[ * 100 fishermen can fish either in the ocean or in a small lake: `\(100 = X_o+X_s\)` * In the ocean every fisherman fish 50 fishes: `\(Y_o=50X_o\)` * In the lake the number of fishes fished per fisherman depends on the number of fishermen: `\(Y_s=90X_s-X^2_s\)` * Each fisherman chooses the place where he can fish more fishes. * In equilibrium, each fisherman will fish the same number of fishes in the ocean and in the lake: `\(\frac{Y_o}{X_o}=\frac{Y_s}{X_s}\)` ] .col-6[ `\begin{align*} \frac{50X_o}{X_o}&=\frac{90X_s-X^2_s}{X_s} \\ 50&=90-X_s\\ X_s&=40 &X_o&=60\\ \end{align*}` The fishermen fish `\begin{align*} Y_s&=3600-1600=2000 &Y_o&=50\times 60=3000\\ Y&=5000 \end{align*}` Is that efficient? ] ] ??? # Common Property Resources .col-7[ Suppose that the fishermen are part of a large firm that is planning to use the lake: `\begin{align*} Y&=50X_o+90X_s-X_s^2\\ 100&=X_s+X_o\\ Y&=50(100-X_s)+90X_s-X_s^2\\ &=5000-40X_s-X_s^2\\ \frac{\partial Y}{\partial X_s}&=40-2X_s=0\\ X_s&=20 &X_o&=80\\ \end{align*}` The fishermen fish `\begin{align*} Y_s&=90\times 20-400=1400 &Y_o&=80\times 50 = 4000\\ Y&=5400 \end{align*}` ] --- # Common Property Resources .row[ .col-6[ ![](img13/fish.png) ] .col-6[ * Without controls, the fish/month equals `\(F_C\)`, satisfying `\(MC = MB\)`. * As a result, the fisherman's private cost understates the true cost. The efficient ratio fish/month is equal to F*, satisfying `\(MSC = MB\)`. Because public resources are non-rival and non-exclusive, they often face an overuse, since users only consider their private costs (tragedy of the commons). ] ] --- class: practice-slide # 8. .col-8[ Canada’s Labrador Peninsula (which includes modern-day Newfoundland and most of modern-day Quebec) was once home to an indigenous group, the Montagnes, who, in contrast to their counterparts in the American Southwest, established property rights over land. This institutional change was a direct result of the increase in the fur trade after European traders arrived. a. Before European traders came, the amount of land in the Labrador Peninsula far exceeded the indigenous people’s needs. Hunting animals specifically for fur was not yet widely practiced. What can you conclude about the relative scarcity of land or animals? Why? ] ??? a. Land and animals were not scarce as the supply of them exceeded the demand. --- class: practice-slide # 8. .row[ .col-6[ b. Before the European arrival, land was commonly held. Given your answer in part a, did the tragedy of the commons play out for the indigenous Montagnes? (Remember, air is also commonly held.) c. Once the European traders came, the demand for fur increased. Do you expect the tragedy of the commons to play out under these circumstances? Why or why not? ] .col-6[ d. The Montagnes established property rights over the fur trade, allocating families’ hunting territory. This led to rules ranging from when an animal is accidentally killed in a neighbor’s territory to laws governing inheritance. Why did the Montagnes create property rights only after the European traders came? ]] ??? b. The tragedy did not play out because given their demands their animal resources could not be exhausted. c. Yes, the increase in the demand meant that more animals were killed than were naturally replenished, putting the tragedy into action. d. The danger of resource exhaustion (and the increase of the value of furs) generated the incentive to forge property rights. The benefits of property rights exceeded the costs. The Montagnes established property rights to avoid the tragedy of the commons. --- ## Solutions to The Tragedy of the Commons .row[ .col-5[ * Private property (exclusivity) * Central planning (the planner needs to know everything) * Pigouvian tax * Certificates (the government must know the optimal amounts) ] .col-7[ ![](img13/c18-02.png) ]] --- class: practice-slide # 9. .col-8[ Suppose that you and three roommates are living in an apartment with a common area for living, dining, and cooking. Do you suppose that a “tragedy of the commons” outcome is a likely result without some rules regarding cleaning? What rules would you propose instituting? ]