1. It is hard to calculate the number of permits there should be. SHADOW PRICING is subjective.
2. If the PRICE ELASTICITY OF DEMAND for the good is inelastic, there will only be a small fall in demand from polluting products. (L4+ however, significant revenue is raised, so its effectiveness depends on what the objective was in the first place. Was it to raise revenue or reduce pollution?).
3. It is expensive for the government to ENFORCE the permits. For example, it may be hard to accurately attribute pollution to one particular firm and then you must consider the opportunity cost of the money spent enforcing.
4. Should permits be TRADEABLE? For example, if one firm becomes very efficient another firm may just buy these permits and the overall level of pollution remains the same.
5. The increase in BUSINESS COSTS caused by the tradeable permits may reduce UK competitiveness. (L4+ it depends if the permits are internationally applied).