Abstract
The distortionary effect of upstream petroleum taxation has been discussed extensively by economists. The literature however, has largly neglected the Production Sharing Contract (PSC) which is widely used by the internationl petroleum industry. We examine how a PSC can distort the optimal time path of production from an oil reservoir. To do that, we use optimal control theory and solve the problem with Hamiltonian function. We show that, regardless of the contract parameters, a PSC always distort the time path of production unless the oil price changes at the rate of interest rate.
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Notes
- 1.
There is often a limit as to the proportion of oil available each year for the operator to recover its costs. This is called cost recovery limit. Uncovered costs are usually carried forward to future years.
- 2.
Usually the operator also pays the normal business taxes such as the corporate income tax.
- 3.
See Smith (2012) [3] for a detailed literature review.
- 4.
In this simplified study, this constraint is a unique ratio of yearly depletion, while in reality it should be at least 3 different constraints depending on the life phases of the field, i.e. build up, plateau and declining phase.
- 5.
There is a controversy over the nature of Maximum Efficient rate (MER). Some authors consider it as a pure engineering factor while the others believe it is an economic engineering element.
- 6.
To avoid solving a complicated differential equation, we assumed that the production function has an exponential form \(y(t)=e{}^{\theta t}\). This form is fairly compatible with the realities of the industry, in which, in the first period, buidup, the production increases exponentially and then remains stable in the peak for a period of time and finally decreases exponentially. Accordingly, \(\theta \) would have 3 different values during the life cycle of the field production: For \(0\le t\le t_{1}\), build up period, \(\theta >0\), For \(t_{1}\le t\le t_{2}\), plateau period, \(\theta =0\), For \(t_{2}\le t\le t_{3}\), declining period, \(\theta <0\).
- 7.
We assume that \(\lambda ^{^{\prime }}(t)=\varepsilon \lambda (t)~\) and \(e^{rt}\lambda (t)=\phi \). The first assumption is true since from Hamiltonian function we know \(\lambda (t)=\frac{\partial H}{\partial P}\). In fact, the Lambda represents the shadow price of the depletion rate. We know that the shadow price of the depletion rate decreases as the reserve decreases over the time. We can consider an exponential form for the Lambda as follows: \(\lambda (t)=e^{\varepsilon t}\). If we take derivative from both side we get \(\lambda ^{^{\prime }}(t)=\varepsilon \lambda (t)\). Furthermore, we assume that: \(\left( p^{\prime }-rp\right) =P\), \(\left( A\left( v\left( t\right) \right) -c^{(1,1)}+\phi \left( \frac{\varepsilon }{\rho }-1\right) +rc^{(1,0)}-c^{(0,1)}\right) =K\), \(\left( \left( 1-\alpha \right) \left[ 1-\left( 1-\beta \right) \left( \gamma +\left( 1-\gamma \right) \tau \right) \right] \right) =G\).
References
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Farimani, F.M., Mu, X., Taherifard, A. (2017). The Distortionary Effect of Petroleum Production Sharing Contract: A Theoretical Assessment. In: Dörner, K., Ljubic, I., Pflug, G., Tragler, G. (eds) Operations Research Proceedings 2015. Operations Research Proceedings. Springer, Cham. https://doi.org/10.1007/978-3-319-42902-1_75
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DOI: https://doi.org/10.1007/978-3-319-42902-1_75
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