Economic Profit and the Return on Invested Capital In my finance classes, I always learned that the a firm earning an "economic profit" is one for which its return on invested capital (ROIC) is greater than it's opportunity cost of capital (usually calculated using the Weighted Average Cost of Capital). But, in my economics classes, I learned that economic profit accrues to a firm that has the ability to price above marginal cost (the demand curve for its product is not infinitely elastic).

Are these two definitions compatible? Is there a way to connect the two? The reason for my question is that I have noticed situations in which the two don't concur. For example, oil companies have negligible market share (when considered globally; e.g. Exxon, the largest U.S. oil major, has about 3% market share - will try to find the reference for this, can't currently remember) and sell a commodity product, and so that's pretty close to the "competitive ideal" as depicted in any Intermediate Micro class. However, if you look at Exxon's ROIC, it has at times been in the 30% range, much higher than any reasonable estimate of WACC (usually around 7-12%). So there appears to be a discrepancy between two different measures of "economic profit".
Both of them are consistent. The economic profit is the total revenue $TR$ minus total cost $TC$ but in economics costs must include also opportunity costs not just accounting ones.

However, for all standard market structures  $TR&gt;TC$ happens only if the marginal revenue or price  $P$ is above marginal costs $MC$.

Also if there is positive economic profit then also return on the capital will be higher than opportunity cost of that capital, because by definition such profit must be higher than the minimum necessary to compensate for the opportunity cost.

So it’s not that the definitions are inconsistent they are just different results based on the same principle. However, if you would try to calculate the true economic profit by different estimation methods you could get different answers because some opportunity cost might be not easy to observe. For example, weighted average costs of capital (WACC) is a crude way how to estimate opportunity cost it’s not the definition of it. Also many inputs in WACC are only proxies not actually directly observable variables.

Now turning attention to your example it’s simply not true the demand for oil is elastic or that oil market is perfectly competitive market. Due to organizations as OPEC oil market was for long time almost monopolized and even though the strength of OPEC decreased in recent years I would still put it somewhere more close to oligopoly. It’s definitely not even close to perfectly competitive market which requires many sellers not just few key players. Also perfect competition requires (virtually) no barriers to entry and in oil industry the entry barriers can be high. 

Moreover, demand for oil is also very inelastic. Unfortunately even now in 21st century our civilization crucially depends on fossil fuels to run. Oil is still virtually a necessity and demand for it is highly inelastic. In fact if you try to survey the literature on google scholar by checking for elasticity of oil demand you find that most mean estimates report elasticity less than 1 and many close to 0.1 which is very small. In such setting in most market structures you get a room for significant economic profit as market power varies inversely with elasticity of demand.