Since the emissivity of the earth with the greenhouse effect is reduced more than the absorptivity is reduced, the equilibrium temperature increases.
Without a definition of the vague notion “the equilibrium temperature” I’m afraid I’m unable to agree with this. Please either cite the page number where this term is defined or give your own definition.
As it stands it could mean anything, and with some of those meanings your claim about it is wildly inaccurate.