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Resources and Reserves: Capital-to-Output Ratios and Discoveries

Capital-to-Output Ratios

Resource base is important in selected energy categories of IFs: conventional oil, natural gas, coal, hydroelectric power, and unconventional oil.  Resources are not important in the nuclear category, which represents an undefined mixture of burner, breeder and fusion power.

Resource costs, as represented by the capital required to exploit them, increase as resource availability in the resource-constrained categories decreases.  The capital-to-output ratio captures the increased cost.  Kalymon (1975) took a similar approach.

More specifically, the capital-to-output ratio (QE) increases in inverse proportion to the remaining resource base (as the base is cut in half, costs double; as it is cut to one fourth, costs quadruple).  The model multiplies the initial capital output ratio by the initial resource base (RESOR) times a multiplier (RESORM) by which a model user can exogenously increase or decrease model assumptions.  It then divides that product by initial resources minus cumulative production to date (CUMPR).

Total available resources by energy type, ResorTot, are calculated as:



  • resor and resoruncon are exogenously assumed levels of the ultimate amount of conventional and unconventional forms of each energy type.  There is no assumption about conventional resources for nuclear and only oil and gas include unconventional resources
  • resorm and resorunconm are multipliers that can be used to change the amount of assumed ultimate resources by energy type

All energy types begin with basic capital-to-output ratios, BQE and BQEUC.  These are initially set equal to the same values of QE and QEUNCON, which are derived in the pre-processor, and then evolved according to exogenous assumptions about technological advance for each energy type:

eq97 [1]


Recall that technological improvements result in declining amounts of capital required for each unit of energy produced.

The initial translation of this basic capital-to-output ratio to the value actually used to determine energy production varies by energy type.

This is most straightforward for nuclear and unconventional energy, which do not take into account remaining resources:



  • e is nuclear
  • qem is an exogenous multiplier



  • e is oil or gas
  • qeunconm is an exogenous multiplier

For hydro and other renewables, QE depends upon the remaining resource, which is defined as the difference between the total resource available and a moving average of the difference in production vis-à-vis production in the first year.  In other words, it is not cumulative production that is important, but rather the portion of resources used annually.






  • e = hydro or renew

For oil, gas, and coal, the logic is similar, but the definition of remaining resources is somewhat different: 




Furthermore, the capital-to-output ratio is calculated as a moving average




  • e is oil, gas, or coal


Energy reserves decrease with production and increase with discoveries, the latter of which are limited by remaining resources and other factors.  This only applies to oil, gas, and coal.


The rate of discovery, rd, is initially computed as a function of a number of factors related to global energy prices, remaining resources, global and domestic production, and several exogenous assumptions



  • e = oil, gas, coal
  • rdm is a country and energy-specific exogenous multiplier
  • rdi_aug is an energy-specific factor driven entirely by exogenous assumptions about initial rates of discovery, rdi , and annual increments, rdinr :


  • wepterm is a global factor driven by the growth in world energy prices from the first year and an exogenously defined elasticity, elasdi


  • reterm is a country and energy-specific factor representing an average of a country’s remaining resources as a share of original resources and its share of current production


A further assumption is that the rate of discovery cannot exceed 4 percent of the remaining resources in a country, where remaining resources are specified as:



  • e = oil, gas, coal
  • For oil the amount of unconventional oil in ResorTot is also affected by the parameter enresunce [2]



[1] There used to be an additional impact of ICT broadband that would further reduce the BQE for other renewables, but that is currently not active in the model. 

[2] This only affects Canada, which has a value of enresunce = 0.3. Why this is not included in the QE calculations is unclear.