Explain the following:

a. Why an emissions tax smaller than or greater than the marginal social cost at QOPT leads to a smaller total surplus compared to the total surplus generated if the emissions tax had been set optimally

b. Why a system of tradable emissions permits that sets the total quantity of allowable pollution higher or lower than QOPT leads to a smaller total surplus compared to the total surplus generated if the number of permits had been set optimally

c. How a carbon tax, which is a tax on carbon emissions, would encourage consumers to use more renewable energy sources