APPENDIX Terms-of-Trade Effects in the Endogenous Input Price Case
This appendix considers how the underlying model parameter values determine the terms of trade effects and the socially optimal input subsidy in the endogenous input price model analyzed in Section III. This depends on the magnitude and sign of the term ρ / σ in equation (19) in the text.
To begin with, consider σ, which is the elasticity of input quantity x with respect to the input subsidy rate s. A closed-form solution for this parameter can be obtained by differentiating the Russian producer’s first-order condition with respect to s, which yields the following:
by the concavity of the profit function.20 If s < 1, then σ > 0.
The other parameter in equation (19) that needs to be considered is ρ, which depends on
where qx and qs were obtained by differentiating Ukraine’s reaction function (17). It is apparent from (22) that a sufficient (but not necessary) condition for ρ > 0 is that
where θ is a measure of the curvature of the demand function. For a linear demand function, θ = 0, and this condition is not satisfied. For a constant elasticity demand function with elasticity (defined to be positive) ∊, θ = - (∊ + 1); therefore, equation (24) is satisfied if ∊ > 1.
If s < 1 and hence σ > 0, as shown by equation (19), whether the socially optimal subsidy rate is positive or negative depends on how changes in the input subsidy rate s affect the terms of trade q, an effect measured by parameter ρ. If an increase in s improves the terms of trade by lowering q (implying that ρ < 0), this raises tax revenue by reducing the fiscal cost of the subsidy sqx, increases social welfare, and ensures that the socially optimal subsidy is strictly positive. A necessary (but not sufficient) condition for ρ < 0 and hence s > 0 is that θ > -2, which means that the demand function is sufficiently concave. A linear demand function satisfies this condition (θ = 0); unfortunately, the sign of the socially optimal subsidy rate is nevertheless ambiguous. If an increase in s worsens the terms of trade by raising q (implying that ρ > 0), this lowers tax revenue by increasing the fiscal cost of the subsidy sqx, lowers social welfare, and makes the sign of the socially optimal subsidy ambiguous. A sufficient (but not necessary) condition for ρ > 0 is that θ < -2. The constant elasticity demand function satisfies this condition; hence, the sign of the socially optimal subsidy rate is ambiguous in this case as well.
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Clinton R. Shiells is a Senior Economist in the IMF Institute. Special thanks are due to Michael Keen for his guidance and encouragement throughout the preparation of this paper. The helpful comments and suggestions of Dale Chua. John Dodsworth, Mark Flanagan, Tim Kehoe, Goohoon Kwon, Bogdan Lissovolik, Miguel Messmacher. Vincent Moissinac-Massenat, Alex Pivovarsky, Tom Richardson, David Robinson, lhor Shpak, and two anonymous referees are also gratefully acknowledged.
The CIS is an economic alliance of 12 of the former Soviet republics: Armenia, Azerbaijan, Belarus, Georgia, Kazakhstan, the Kyrgyz Republic, Moldova, Russia, Tajikistan, Turkmenistan, Ukraine, and Uzbekistan.
Baer, Summers, and Sunley (1996) discuss why use of the destination principle would be desirable for the CIS countries. They explain that the literature on the conditions under which origin and destination principles are equivalent (which includes Whalley, 1979; Grossman, 1980; Berglas, 1981; Lockwood, de Meza, and Myles, 1994; Genser, 1996; and Keen and Lahiri, 1998) has limited applicability to the CIS countries. Chapter 17 of Ebrill and others (2001) considers more generally the merits of destination-based versus origin-based VAT regimes.
Keen and Wildasin (2004) consider the desirability of production efficiency for the attainment of Pareto-efficient international tax regimes in the presence of national budget constraints. Production efficiency is desirable in the presence of national budget constraints under certain conditions related to the availability of explicit or implicit devices for reallocating tax revenue across countries.
Dodsworth, Mathieu, and Shiells (2002) discuss the role of Russia and Ukraine in the energy markets of the CIS countries at greater length.
According to data provided by Russian authorities, Russia exported 39.7 billion cubic meters of gas, 4.0 million tons of crude oil, and 2.1 million tons of oil products to Ukraine in 2000. However, problems of comparability exist among these figures, official Ukrainian statistics, and the oil and gas balances in Tables 2 and 3.
The increase in crude oil imports in 2001 shown in Table 5 appears to reflect Ukraine’s success in securing sufficient crude oil imports for its refineries by offering oil exporters in Russia and Kazakhstan a stake in the country’s refineries (see U.S. Department of Energy, 2003).
Other factors cited as accounting for the large budgetary arrears of Naftogaz include lags between the time when payments to the budget and external suppliers are due and when consumer payments are received, as well as the increase over time in the share of the transit fee to be transferred to the budget.
Prices of oil and oil products have largely converged to world market prices, in contrast to natural gas and electricity prices, which remain well below Western European levels. In the case of gas, it can be argued that this situation involves an element of implicit subsidization, even after including Russian taxes on exports (see Dodsworth, Mathieu. and Shiells, 2002).
If Russia has market power, it could simply replace the VAT on oil exports with an export tax, notwithstanding concerns regarding the intensification of trade protection. For an exporter, the combination of a consumption tax (for example, VAT on a destination basis) and an export tax is equivalent to a production tax (for example, VAT on an origin basis). Alternatively, the Russian firms could collude with the government and charge a monopoly export price.
In fact, as noted above, gas prices paid by consumers are set administratively in Ukraine and fall well short of the levels that would be chosen by a monopolist. The optimal tax/subsidy measures derived below would have to be accompanied by a variety of supporting measures to achieve the first-best social optimum.
If Ukraine were assumed to be the leader, results obtained by Lahiri and Ono (1999) suggest that the optimal input subsidy would be unambiguously positive, which would considerably simplify the analysis in this paper.
If there were two competing foreign producers and one monopolistic seller, it might be more appropriate to assume that the domestic seller is the leader.
It may be more natural to think of the Russian producer as choosing the export price to maximize profits, incorporating the seller’s reaction function for export quantity as a function of export price (and tax parameters). An equivalent but more tractable approach is to assume that the Russian producer chooses export quantity to maximize profits, incorporating the seller’s reaction function for export price as a function of export quantity (and tax parameters).
The assumption that the producer and seller take the VAT and credit rates as exogenous is consistent with the view that the firms are unable to influence these rates. If the firms are able to influence the rates, the strategic interaction between the firms and the governments should ideally be incorporated into the model. This would considerably complicate the model and is beyond the scope of this paper.
“The revenue function in (8) differs slightly from the revenue function in (6), reflecting the difference between a credit for Russian VAT and an input subsidy.