A consumer can borrow or lend freely at the market interest rate of r=100% per period. [If it's helpful, think of the "period" as being a few decades.] Her utility function is:

U = ln(c_t) + (1/2)ln(c_t+1)

She earns Y_t=100 and Y_t+1=100. But in periodt+1 she will have to pay a tax of T_t+1=40.

If she's maximizing her utility function subject to the IBC, how much will she consume in periodt?