I know @Kevinmilligan will cringe, but I will tweet an example of a Carbon Tax with lump-sum "Rebate" at an Intermediate Microeconomics level (1/4)

(Note: this is mainly just me prepping an example for a future in which I teach Intermediate Micro) #teachecon Suppose we have a consumer that only consumes 2 goods (or two groups of goods):
1. a carbon intensive good, y
2. a carbon neutral good, x
And the consumer has an income of I
(2/4)