The utility function of a consumer is given by U = log(b) + log(c) where b and c are the consumption levels of barley and corn. Assume that the price for both goods is $1 and that the consumer has an income of $100. Assume that the government introduces unit taxes of $1 on barley and corn such that the after-tax price for barley and corn is $2 (hence, the consumer bears the economic incidence of the tax).
Calculate the optimal quantities of barley and corn both before and after the implementation of the tax.
Use the inverse elasticity rule to conclude that both goods should be subject to the same level of tax. (Hint: calculate the elasticities at the equilibrium before the tax)
Calculate the unit tax required to obtain a level of revenue of R = 60 using the fact that the demand for barley (corn) is given by b = 50/(1+tb) (c=50/(1+tc)).