DISCUSSION PAPERS IN ECONOMICS

DISCUSSION PAPERS IN ECONOMICS Working Paper No. 99-30 The Importance of Agenda and Willingness to Pay Nicholas E. Flores Department of Economics, University of Colorado at Boulder Boulder, Colorado December 1999 Center for Economic Analysis Department of Economics University of Colorado at Boulder Boulder, Colorado 80309 1999 Nicholas E. Flores

The Importance of Agenda and Willingness to Pay Abstract This paper links the spatial model of voters preferences to the willingness to pay model of public goods provision. The willingness to pay approach, which is commonly used in benefit-cost analysis, is free from a specific cost provision schedule. Freedom from a specific cost schedule facilitates a wide range of choices for a monopoly agenda setter, including budget maximization and profit maximization, within a single model. Like the spatial model, the willingness to pay model allows for a clear graphical analysis. Interdependence of multiple good preferences is analyzed using substitute/complement relationships. These relationships can be used to predict how goods may be bundled to ensure passage or defeat.

Introduction The importance of the agenda is a well-studied phenomenon in the public choice literature. Much of our understanding of agenda effects has resulted from the application of spatial models to different formulations of the collective choice problem. This paper departs from the spatial approach and instead uses the willingness to pay framework to analyze the importance of agenda. 1 Both the willingness to pay framework and spatial models formulate the choice problem as that of a utility-maximizing agent facing an income constraint and a collective goods constraint. 2 While both generate the same individual decisions in the same circumstances, the analytical structure of the two approaches differ. The spatial approach considers what public goods choice would be made if the individual were able to select the level of public goods subject to an individual provision cost schedule. 3 The willingness to pay approach considers what individual price would be charged to induce the consumer to choose the constrained level of provision if the individual were able to freely choose the level of public goods. In the first case, a set of private levels of public goods is used as a point of reference and in the second case a set of private prices is used as a reference point. Using the willingness to pay framework in a one-dimensional public goods setting, the paper analyzes the monopoly agenda setter problem of Romer and Rosenthal (1978), Romer and Rosenthal (1979) and revisits the utility-maximizing bureaucrat discussed in Niskanen (1975). The paper then considers the two extremes of the utility-maximizing agenda setter, budget maximizing and profit maximizing, and characterizes the agenda setter's optimal profit maximizing solution. The willingness to pay framework allows a clear graphical analysis of the choices facing a utility-maximizing agenda setter. In a multi-dimensional setting, the paper uses the willingness to pay framework to 1 The willingness to pay framework is the standard approach used in benefit-cost analysis. 2 Still earlier applications of the same type of utility maximizing model can be found in the rationed goods literature. An early summary of this literature can be found in Tobin (1952). 3 Other variations include selecting the mix of public goods given an already determined budget or selecting the budget given an already determined mix of public goods. 1

decompose multi-dimensional bundles into sequences of single-dimensional changes. This allows the multi-dimensional properties of willingness to pay to be more carefully examined and related to unconstrained, utility-constant demands for the public goods. Using results from Carson, Flores and Hanemann (1998), the paper shows that expenditure approval with bundling is less likely if the unconstrained demands for public goods are Hicksian substitutes and more likely if they are Hicksian complements. Thus qualitative predictions of individual voter behavior are available without imposing separability. Moreover, the issue of surplus trading across dimensions is placed in an easily interpretable framework. Public goods with different magnitudes of willingness to pay relative to costs may be combined to assist in the passage of some measures and the failure of others. Finally, the paper provides a multi-dimensional analog of the choices facing the utility-maximizing agenda setter who has knowledge of voters' preferences. An Economic Model of Individual Choice Suppose that individual agents have non-satiable, strictly convex preferences over n market goods and k public goods and that these preferences are differentiable. The k-dimensional vector of public goods will be denoted Q and the n-dimensional vector of market goods will be denoted X. Equivalently, individual agent preferences can be represented by a strictly increasing, strictly quasi-concave utility function U(X,Q). The levels of private goods are individually chosen while the levels of public goods are collectively provided. Let y denote current disposable income which is simply income less payments for the current public goods level, Q 0, and p denote the vector of prices for the n market goods. The choice problem is to maximize utility subject to market prices, disposable income and the current level of public goods. 4 X m (p,q 0,y) is the vector that solves the maximization problem, or ordinary Marshallian demands, and U 0 = U(X(p,Q 0,y),Q 0 ) is the maximum obtainable utility. Of primary interest is the characterization of the optimal choice when deciding whether to vote yes or no for a change from the status quo level of public goods and the choice of agenda is 4 It will be assumed throughout this paper that the alternative to the proposed change is the current level of public goods provision/expenditures. Relaxing this assumption and allowing a different reversion level shifts the decision to an analysis centered around the reversion level. 2

outside of the agent's control. 5 One can think of the agenda coming from a variety of sources such as a monopoly agenda setter, a committee, or a group petitioning for a referendum. In any case, the agent has no input into what goes onto the agenda. The decision rule is passage by majority support of voters. Given that agents are maximizing utility and have no incentive to act strategically, the optimal decision rule is to vote for any proposition that results in a utility gain and vote against any proposition that results in a utility loss. Agents are indifferent between propositions that leave utility unchanged which makes either voting for the proposition or against the proposition optimal. It is assumed that in the situation of indifference, the decision rule is to vote for the proposition. Spatial analyses found in the public choice literature are centered around the concept of voters' ideal or preferred points of provision. The agent's preferred point of provision can be obtained by carrying out the mental exercise of deriving what level would be chosen by the agent if the choice of both the market and public goods were at his or her disposal. The preferred point is simply the mix of private and public goods chosen when the consumer is maximizing utility subject to before-tax income, market prices, and individual costs for each public good. 6 With a known provision schedule that yields a convex budget set for market and public goods, the class of preferences considered here provides a unique preferred point. With the preferred point in mind, the constrained utility analysis can be transformed into a spatial analysis whereby the utility ordering of possible combinations is equivalently represented by a function that is decreasing in movement away from the preferred point. In the case of a single market and public good, this concept is represented in the following two graphs. The first graph is the typical indifference curve graph showing that the utility-maximizing choice is (X *,Q * ). The second graph shows the relationship between the level of Q chosen and the maximum 5 The vote is a take-it or leave-it proposition and the analysis is a one-shot situation. Hence there is no incentive to vote strategically, leaving agents to vote sincerely. 6 There are other variations such as the preferred point obtained after a budget has been set and the individual chooses the mix of public goods. In these cases, the constraint is different in that the allocation between market goods and public goods has already been made. 3

obtainable utility for each Q. This relationship can be equivalently rewritten as a function of distance from the ideal point, Q *. U * U 0 As Figure 1.b. shows, the space of possibilities is partitioned into an acceptance region and a rejection region. The acceptance region consists of those alternatives located between the points of indifference, Q 0 and Q 0 +, or all of those points that would constitute a utility gain; the rejection region consists of those points located beyond the indifference points in the respective directions or those points that would constitute a utility loss. The decision rule is a simple spatial rule: vote yes when the proposition is located in the acceptance region and no if the proposition is located in the rejection region. An alternative individual decision rule is the comparison of willingness to pay for the 4

specified change with the individual cost of provision. 7 Willingness to pay is the amount of income foregone that would hold utility at the status quo level with the increased level of public goods, U 0 = U(X(p,Q 1,y-WTP),Q 1 ). Here the decision rule is to vote yes for the proposed change if the individual cost is less than or equal to willingness to pay and vote no if the individual cost exceeds willingness to pay. As in a spatial analysis, the acceptance region signals a utility gain relative to U 0 and the rejection region signals a utility loss. Figure 2 shows willingness to pay for a typical individual. The class of preferences under consideration guarantees that individual willingness to pay is strictly concave for increases in Q. At Q', the voter would agree to the provision increase if the increase cost less than P * and vote no if the cost were any greater. From an analytical perspective using a willingness to pay analysis is different from the spatial analysis. Knowledge of the distribution of voters' willingness to pay imparts knowledge of what price could be charged for a specified change while attaining majority approval whereas the spatial analysis imparts information that is relative to a price schedule. The Monopoly Agenda Setter and Willingness to Pay Building on work by [Niskanen (1971), Niskanen (1975)], [Romer and Rosenthal (1978), Romer and Rosenthal (1979)] provided a spatial analysis in the situation of a budget-maximizing agenda setter who presents a budget for consideration to voters who have different ideal points. 7 For simplicity, only increases from the status quo will be considered. The analysis is easily generalized in order to include decreases by using a willingness to accept compensation criterion along with the willingness to pay criterion for increases. 5

The agenda setter knows the voters' preferences which imparts knowledge of voters' preferred points (as well as willingness to pay). The setter also knows the cost of provision. 8 The Romer and Rosenthal analysis showed that the optimal agenda setting choice is either the reversion level (status quo level) or the highest provision level that would engender majority support. The choice depends upon the status quo provision level and voters' preferences. In the latter case, the decisive voter is left indifferent between the status quo level and the proposed agenda. Figures 3 and 4 provide graphs of the preference functions of three voters in two different situations. Q BM is the equilibrium point chosen by the agenda setter. In Figure 3, voter B is decisive and in Figure 4, voter A is decisive. 8 Given the budget maximizing assumption, voters' knowing or not knowing the cost provision is unimportant. 6

Niskanen (1975) discussed the plausibility of his 1971 budget-maximizing model and provided an alternative model of a utility-maximizing bureaucrat who provides some singledimensional output to the government and is subject to review by a government board. In the alternative model, the bureaucrat knows the relationship between the quantity demanded and the cost of provision, but the review board members necessarily do not know the minimum cost of provision. Niskanen provided a specific utility function with arguments of the bureaucrat's income and non-monetary perquisites. In the model, both income and non-monetary perquisites are functions of Q and the bureaucrat's discretionary budget, B-C, where B is the maximum budget that would be passed and C is the minimum cost of providing Q. Niskanen's discussion of the qualitative effects of changing the model's parameters was essentially an analysis of the tradeoffs between higher output and discretionary budget. However, his analysis explicitly excluded the possibility of a monopoly supplier and therefore total surplus extraction was not a possibility. By using the willingness to pay framework, the choices facing a utility-maximizing agenda setter can be graphically analyzed. Suppose that voters' preferences as well as provision costs, are known by the setter. Voters do not know the minimum cost of provision and vote their preferences. As noted above, the agenda setter's complete knowledge of voters' preferences can be translated into knowledge of the median willingness to pay distribution for every alternative 7

level of Q. Figure 5 shows willingness to pay for three voters and the cost of provision per individual which is assumed to be convex in costs. 9 Median willingness to pay is given by voter B's willingness to pay curve from Q 0 to Q' and by voter A's willingness to pay curve from Q' to Q BM. Costs Q 0 Q' Q BM From the Romer and Rosenthal analysis, the median willingness to pay will equal the cost of provision in the budget-maximizing case which is given by Q BM in Figure 5. This follows since at the equilibrium allocation derived in their analysis, the decisive voter is left indifferent. However for those points where median willingness to pay exceeds provision costs, the monopoly agenda setter has the option of charging more than provision costs and up to the median willingness to pay. 10 While total revenues will still be greater at Q BM (and hence the budgetmaximizing agenda setter would still choose this point), the possibility of enjoying discretionary budget adds an interesting dimension. As an extreme case, suppose that the agenda setter is a profit maximizer, i.e. the agenda setter is concerned only with maximizing discretionary budget. 11 In this case, the agenda setter 9 For simplicity, it is assumed that the cost is shared equally by each individual. 10 Throughout my analysis, it is assumed that at least the median voter's willingness to pay for small changes exceeds provision costs. A voter who finds provision too high at the status quo level would have a willingness to pay curve that is still concave in Q, but lies below the cost curve at all points greater than Q 0. Without any subsidization, such a voter would only vote for decreases and then the trade-off would be between the reduction in taxes and the reduction in Q. 11 Like the decision made by the consumer, the agenda-setter also must face the status quo. Therefore when refering to profit maximization, it is in reference to the status quo level of profits; the setter is deciding on maximum profits in addition to the level of profits at the status quo. 8

will choose Q to maximize the difference between median willingness to pay and the cost of provision. That is to say, the setter's objective is to choose Q in order to maximize WTP m (Q) - C(Q) where WTP m (Q) is the median willingness to pay function. The characterization of the point the agenda setter presents voters will depend upon the median willingness to pay function. First consider the case of a single voter having median willingness to pay for every alternative Q. In this case, the median willingness to pay function is differentiable and concave in Q. Therefore the optimal solution can be characterized by tangency conditions. The profitmaximizing agenda setter will produce at the level where marginal willingness to pay equals the marginal cost of provision. In Figure 6, this point is given by Q PM. Q 0 Q BM Assuming that Q is a normal good, the profit maximizing outcome will be less than the median willingness to pay voter's ideal point. This follows since at both the profit maximizing outcome and the ideal point, the ratio of marginal utility of the market good to marginal utility of the public good equals the ratio of the market good's price to the marginal provision cost. In both cases, the move represents a decrease in the shadow price relative to the initial point since there is an increase in Q. 12 The reduction in the shadow price implies a positive income effect that is realized in the income-constant, ideal point analysis, but is unrealized in the utility-constant 12 The shadow price p * is the price of Q that would induce consumption of the constrained\market bundle (X,Q) if both were chosen by the consumer. 9

analysis. 13 Figure 7 shows the ideal point, Q *, and the profit maximizing point, Q PM, for the median voter. In situations where the median voter changes with Q, median willingness to pay is still continuous, but no longer differentiable. Therefore all local interior optima and non-differentiable points must be evaluated. As the example shown in Figure 8 demonstrates, the profit maximizing point can occur at the intersection of two voters' willingness to pay curve. Q 0 Q BM Realistically, most bureaucrats will fall in between the extremes of budget-maximizing and profit maximizing. This leaves us with some utility-weighting scheme similar to the one found in 13 Recall that the willingness to pay analysis is utility-constant and therefore changes in consumption are along the same indifference curve. The ideal point analysis is income-constant and changes in consumption generally imply changes in utility. 10

Niskanen's analysis whereby the agenda setter trades off the level of provision with discretionary budget. Depending upon the setter's preferences, which may in turn depend upon the rules imposed on the setter, the optimal choice will occur somewhere between the extremes of budget maximizing and profit maximizing. The equivalence of the spatial approach and the willingness to pay framework implies that the two approaches are complementary. As in the case of the spatial analysis, the willingness to pay framework also lends itself to a nice graphical analysis. However, the willingness to pay framework has the advantage of not being subject to a provision schedule. Therefore the case of a utility-maximizing agenda setter is easily handled. The next section provides a multidimensional analysis of willingness to pay and show that simple information regarding substitution and complementarity between public goods gives the agenda setter still more options to obtain a more preferred outcome, from the agenda setter s perspective, by using agenda power. Multi-dimensional Bundling In a multi-dimensional public choice setting, predictions as clear as those from the singledimensional agenda setter models are much more difficult to obtain. Much of the research on agenda control in a multi-dimensional setting can be attributed to MacKay and Weaver (1981), MacKay and Weaver (1983). By imposing sufficient structure, the multi-dimensional analysis becomes more tractable. 14 Rather than imposing structure on the rules of the decision process to demonstrate the importance of the agenda, the focus is on individual preferences. By imposing a substitute or complement condition on the public goods under consideration, bundling affects willingness to pay and in turn influences the voter's decision. Returning to the willingness to pay framework, recall that willingness to pay satisfies the condition U 0 = U(X(p,Q 1,y-WTP),Q 1 ). Willingness to pay can also be represented as the difference in minimal expenditures necessary to obtain utility level U 0 when Q 0 and Q 1 are the respective public goods provision levels: WTP = e(p,q 0,U 0 ) - e(p,q 1,U 0 ). 14 MacKay and Weaver (1981), MacKay and Weaver (1983) provide a sequential analysis where the mix of public goods is selected subject to a budget or the budget is selected subject to a given mix of public goods. 11

This representation has proven invaluable in the public goods valuation research because this difference can be rewritten into a sequence of changes that provides valuable insight. 15 For example, suppose there are three public goods, Q = [q 1,q 2,q 3 ] t where t denotes the transpose. By adding and subtracting the two terms e(p,q 1 1,q 0 2,q 0 3,U 0 ) and e(p,q 1 1,q 1 2,q 0 3,U 0 ), willingness to pay for the multi-dimensional change can be rewritten into a sequence of singledimensional changes: WTP = [e(p,q 0 1,q 0 2,q 0 3,U 0 ) - e(p,q 1 1,q 0 2,q 0 3,U 0 )] + [e(p,q 1 1,q 0 2,q 0 3,U 0 ) - e(p,q 1 1,q 1 2,q 0 3,U 0 )] + [e(p,q 1 1,q 1 2,q 0 3,U 0 ) - e(p,q 1 1,q 1 2,q 1 3,U 0 )]. The first term in brackets is the willingness to pay for an increase in q 1 given the other goods are at the status quo level. The second term is willingness to pay for the increase in the second public good with the higher level of the first good and the status quo level of the third good. The last term is the willingness to pay for the increase in q 3 given the other public goods are at the higher level. For any of the single-dimensional changes, willingness to pay can be rewritten using the fundamental theorem of calculus. Using the first term as an example, e(p, q 0 1, q 0 2, q 0 3, U 0 ) & e(p, q 1 1, q 0 2, q 0 3, U Me(p, s, q 0 0 2 ) ', q 0 3, U 0 ) ds. m Ms q 0 1 q 1 1 Willingness to pay is simply the integral over the marginal change in expenditures with respect to q 1. The assumed convexity of preferences yields a unique set of shadow prices for each public good for any point in the interior of the (X,Q) space. As shown by Maler (1974), the shadow price for each public good is the negative of the derivative of the expenditure function with respect to the good. The set of shadow prices at the status quo public goods level can be interpreted as the set of prices that would induce consumption of the same market goods/public goods bundle when both market and public goods are in the consumer's choice set. The first term 15 The sequence may be written in public goods or prices. Contemporary discussions of non-user values in the environmental goods literature decompose willingness to pay into first a price change and then a quantity change. This decomposition facilitates the use of the weak complementary condition (Maler (1974)). 12

can be rewritten using the shadow price relationship: q 0 1 Me(p, s, q 0 2, q 0 3, U 0 ) ds ' &p ( m Ms m 1 (p, s, q 0 2, q 0 3, U 0 )ds ' p ( m 1 (p, s, q 0 2, q 0 3, U 0 )ds. q 1 1 q 1 1 q 0 1 Willingness to pay for a one-dimensional change is simply the integral over the public good's inverse demand function or equivalently the integral over the good s shadow value. The set of inverse demand functions are functions of market goods prices and other public goods levels and therefore willingness to pay is also a function of these variables. In the cost-benefit literature, much attention has been focused on the relationship between a single public good and market goods while less emphasis has been placed on the relationship between public goods. Carson, Flores and Hanemann (1998) proved several propositions relating conditions from the unconstrained utility-maximization problem to the collective choice problem under consideration here. The propositions referred to below will be stated without proof. The proofs may be found in Carson, Flores and Hanemann (1998). q 1 1 q 0 1 Proposition 4 (CFH): Assume that all rationed goods are (strict) Hicksian substitutes. Then willingness to pay for an increase in q 1 is a nonincreasing (decreasing) function in the levels of q j, j = 1,2,.. k. 16 Proposition 9 (CFH): Suppose there are only two rationed (public) goods, k = 2, and these rationed goods are (strict) Hicksian complements, then willingness to pay for an increase in q i, i = 1, 2 is a nondecreasing (increasing) funnction in the levels of q j, j i. In the case where only two goods are under consideration, k=2, if the public goods are (strict) Hicksian complements, then willingness to pay for an increase in q i is a non-decreasing (increasing) function in the levels of q j, j i. When k > 2 and the goods are Hicksian complements, willingness to pay for an increase in q i may be either increasing or decreasing in the levels of q j, j i. 16 h Two goods (q i, q j ) are (strict) Hicksian substitutes if Mq h where q i is the Hicksian compensated demand. 13 i /Mp ( j (>) $ 0

These two propositions are important in understanding the effect of multi-dimensional bundling at the individual level because they allow for predictions in cases when preferences are not separable. When the goods are unconstrained Hicksian substitutes at the status quo level (subject to facing the individual shadow price), willingness to pay is decreasing in the levels of other public goods. In the case of unconstrained Hicksian complements and k=2, willingness to pay is increasing in the level of the other public good. Given these results, the agenda setter's knowledge of preferences or even just the Hicksian substitute/complement relationship allows for setter gains from the power of the agenda. Suppose that a bureaucrat/agenda setter is considering k distinct projects that can be 0 represented as changes in the levels of Q, [(q 1 6q 1 0 1 ),...,(q k 6q 1 k )]. If one considers each change from the status quo in isolation, then there are k independent valuations for a given voter. 17 A question of interest for the agenda setter is how informative would independent valuations be when proposing multi-dimensional bundles for voters' approval? First assume that the setter only knows each voter's sum of independent valuations and that the cost of provision equals the median voter's sum of independent valuations. If the goods are unrestricted Hicksian substitutes, then the bundle would be turned down by voters. This result follows since willingness to pay for the bundle can be decomposed into the sequence of single-dimensional changes such as the example given above where k=3: WTP = [e(p,q 0 1,q 0 2,q 0 3,U 0 ) - e(p,q 1 1,q 0 2,q 0 3,U 0 )] + [e(p,q 1 1,q 0 2,q 0 3,U 0 ) - e(p,q 1 1,q 1 2,q 0 3,U 0 )] + [e(p,q 1 1,q 1 2,q 0 3,U 0 ) - e(p,q 1 1,q 1 2,q 1 3,U 0 )]. The first term is equivalent to an independent valuation. The second term is willingness to pay for the change in q 2, but with a higher level of q 1 ; the third term is willingness to pay for the change in q 3, but with higher levels of both q 1 and q 2. By Proposition 4 (CFH), willingness to pay for the bundle will be less than the sum of the independent valuations since the second two terms are less than their independently valued counterparts. Therefore, provided that voters' preferences goods. 17 That is to say, one can consider the willingness to pay for each good alone before increasing any of the other 14

are such that the k goods are Hicksian substitutes, the proposed bundle will fail. 18 If the k goods are Hicksian complements and k = 2, then passage is assured since willingness to pay for the bundle will exceed the sum of the independent valuations. However if k $ 3, then the bundling result is ambiguous in that willingness to pay for the bundle may be either greater or less than the sum of independent valuations. By using the results from Carson, Flores and Hanemann (1998), several generalizations are possible. In the case where all public goods under consideration are strict Hicksian substitutes, approval is less likely with bundling. In the case where a pair of public goods under consideration are strict Hicksian complements, approval is more likely with bundling. Therefore with as little information of preferences as whether or not goods are Hicksian substitutes or complements, the agenda setter is able to bundle goods in a manner to influence the outcome in his or her favor. For example, assume that the bureaucrat/agenda setter knows which goods are Hicksian substitutes and which goods are Hicksian complements as well as the distribution of independent willingness to pay for all projects that he may propose. The bureaucrat/agenda setter also has a single preferred project that if proposed alone would fail by a single vote. 19 There are several available options. The most obvious is for the setter to look toward complements that would pass if presented in isolation. Bundling with one or more goods from this set would increase the chance of passage of his preferred project. Another option elucidated by the willingness framework is to trade surplus within substitutes. There may be substitutes that are so highly valued relative to costs that even when bundled with the setter's preferred bundle (that alone would fail), the bundle will engender majority support. 20 18 A good example of what appears to be observable substitution-bundling effects is the California Proposition 128 (Big Green) ballot initiative that went down to defeat in 1990. Some contended that because the initiative simultaneously addressed so many issues, voters were unprepared for so much action at once. 19 Here it is assumed that only the minimal cost of provision is charged subject to a known individual payment schedule. 20 For the sake of simplicity, the possibility of reducing provision in one or more dimensions, which is certainly a possibility if some voters feel provision level is too high for some goods is not analyzed. Adding this dimension does not significantly alter the analysis, but does increase the setter's options. 15

The bureaucrat/agenda setter's knowledge of preferences provides all of the information necessary for manipulating the agenda. First note that the entire space of increases in Q can be partitioned into a majority acceptance region and majority rejection region. This is accomplished by considering the median voter willingness to pay function for any increase in Q and the cost of provision. As in the one-dimensional case, these functions will be denoted WTP m (Q) and C(Q). 21 The partition is given as follows: A = {Q: WTP m (Q) - C(Q) $ 0} R = {Q: WTP m (Q) - C(Q) < 0}, where A is the acceptance region and R is the rejection region. 22 Since the bureaucrat/agenda setter knows voter preferences, he also knows all increases in Q that will pass. Provided that C(Q) is continuous, A is a compact, but not necessarily convex set. 23 Therefore for any continuous function used to define the bureaucrat/setter's preferences, a maximum will exist, although it need not be unique. Again the extremes of budget-maximizing behavior and profitmaximizing behavior can be characterized. A budget maximizer would choose any element in the set M = {Q 0 A: TC(Q) $ TC(Q') œ Q' 0 A} where TC(Q) is the total cost of the additional provision and the profit maximizer would choose any element from the set P = {Q 0 A: WTP(Q) - TC(Q) $ WTP(Q') - TC(Q') œ Q' 0 A}. Because of possible non-convexities, M and P may contain multiple points between which the budget maximizer and profit maximizer respectively would be indifferent. Conclusion Spatial models have broad appeal because of their ability to transform complex choices 21 In the class of preferences considered here, individual willingness to pay is continuous in Q. WTP m (Q) will also be continuous in Q (although not differentiable) because those Q where the median voter changes are intersections of continuous functions. 22 If costs are not uniform across voters, the partition would be defined by the median net willingness to pay function rather than the median willingness to pay function. This follows since different payment schedules may alter the median voter for a particular Q. 23 As noted above, the function WTP(Q) m - C(Q) is continuous. The image of A is closed by definition and bounded above by the maximum of voter incomes. Therefore the image of A is compact and by continuity of WTP m (Q) - C m, (Q), A is compact. 16

into an easily interpretable framework which lends itself to a graphical representation. This paper uses a different, although equivalent, approach to analyze agenda effects by using the willingness to pay framework. In addition to sharing the same underlying utility-maximizing structure, the spatial approach and willingness to pay framework both employ the mental exercise of considering what would happen if the consumer were able to freely choose the levels of public goods. The spatial analysis results in a set of private levels (ideal points) of public goods while the willingness to pay analysis results in a set of private prices for public goods. The willingness to pay framework facilitates a clear analysis of the agenda setter's options and is a nice complement to the spatial approach. In the one-dimensional case, the paper provides an alternative analysis of Niskanen's (1975) utility-maximizing bureaucrat/agenda setter. The willingness to pay framework permits a graphical analysis that allows reference to the extremes of Romer and Rosenthal's (1978,1979) budget-maximizing agenda setter and a profit-maximizing version of Niskanen's (1975) utility-maximizing setter on the same graph. Juxtaposing these two extremes is useful because they bound the choices facing the utility-maximizing setter who is concerned with both the size of the budget and discretionary budget. Using results from Carson, Flores and Hanemann (1998), the paper shows how preference structure can influence voters' decisions in a multi-dimensional setting. Goods that are Hicksian substitutes result in less value for bundled goods than the sum of their independent values and pairs of goods that are Hicksian complements result in more value when bundled than the sum of independent valuations. Thus the agenda setter's knowledge of voters' substitute/complement relationships can provide the margin of victory for the setter's preferred project. Finally, the paper provides a multi-dimensional analog of the choices facing a utilitymaximizing setter. The willingness to pay framework allows a characterization of the setter's choice set which is compact under the condition of a continuous cost function. Therefore if the setter's preferences over the choice set are continuous, a maximum will exist. 17

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