Tax and rebate policy

Consider the following passage from N. Gregory Mankiw's blog, Thursday, February 05, 2009
    My Preferred Fiscal Stimulus
    Regular readers of this blog have a pretty good sense of my policy preferences. But for those occasional readers who might be stopping by, let me reiterate what I would do right now if I were the fiscal king.
    I would institute an immediate and permanent reduction in the payroll tax, financed by a gradual, permanent, and substantial increase in the gasoline tax. I would make the two tax changes equal in present value, so while the package results in a short-run budget deficit, there is no long-term budget impact. Call it the create-jobs, save-the-environment, reduce-traffic-congestion, budget-neutral tax shift.

How would that work?

Complete the first two rows of the table below

Characteristics of the final new optimum with the gas tax revenue exactly matched by a cut in payroll taxes:
(1) Circle the budget line you would be on:  BLa  /  BLb
(2) What would be the value of your optimal MRS? $_________