Firm's output under uncertainty and asymmetric taxation

We consider competitive firms operating under price uncertainty when taxation is asymmetric (i.e. profits are taxed at a higher rate than losses are compensated). In the absence of risk sharing tools, the larger 'gap' in taxation may either lower or increase the firm's optimal output, depending on whether the relative measure of risk aversion is less than or larger than 1. In the presence of risk sharing markets optimal output does not depend on the tax rates, nor on the price distribution or the firm's attitude towards risk. The firm will engage in hedging and, as a result, will lower its expected taxes.