On the Optimal Quantity of Public Goods and Related Issues

This paper seeks to reopen a discussion that the profession has considered settled and closed, namely, the issue of the optimal quantity of a public good to supply. Its focus is on the determination of the optimal quantity to supply of a public good in the Pigovian model as popularized by Musgrave. It argues that the vertical summation of the individual demand curves in the Pigovian model is as inappropriate as the rejected horizontal summation of individuals’ consumption of public goods. The horizontal summation is inconsistent with the physical realities of public good supply suggesting an m-multiple of the quantity that is actually available, which is an illusion. The vertical summation while having the advantage of informing on efficiency taxes and equitable cost sharing formula suffers from the fallacy of aggregation and exaggerates the aggregate demand for public goods, thus misleading supply decisions. This realization comes from reckoning with the basic properties of pure public goods in particular nonrivalry – the joint supply property. Given this property, the paper submits that the optimal quantity of a public good is the largest quantity demanded by any single consumer (individually or as a collective). A corollary of this is that public goods consumption is not validly subject to aggregation by any means. Aggregation is irrelevant and that individual demand curves or schedules are required only for the determination of optimal benefit taxes and equitable cost sharing formula. That is, the individual demand curves for a public good or service should be considered only for the purpose of determining each person’s fair and equitable share of the cost of supply (i.e. based on the individuals’ marginal valuations) as shown in Figure 4. In other words, the so-called (collective) willingness to pay curve is only confusing issues and hence not required. This in no way implies the consumption of separate quantities to be added up. Rather, it stages the consumption of the same quantity by all with different payments that are added up to finance the supply, which conforms to the Pigovian solution and indeed all the solutions that have been advanced. Yet, it is unique from the earlier solutions. An equitable cost sharing formula that guarantees an efficient financing scheme is also proposed. It is a benefit share weighted cost sharing formula, which obviates the potential threat of fiscal drag. It is found that barring information failure, the public budget should ordinarily be enjoying surplus under optimal benefit taxes. That is with optimal benefit taxes, balanced budget is within easy reach with relief for taxpayers in relation to service benefits enjoyed and therefore, less resentment to taxation could be anticipated. These observations and findings need to be given serious thoughts. Though, the rationale for government intervention in an otherwise market economy is primarily seen in market failure, the ultimate justification is the gain in welfare from the achievement of Pareto improvements in resource allocation. It follows that the possibility of further Pareto improvements in welfare must be a welcome development.