Aged consumers expend their entire income (an old-age pension) each period on bus trips and all other goods. The Transport Department proposes to increase the discount for senior fares, thus making bus trips cheaper. If the government promises to limit the effect on government expenditure overall, a lump-sum tax must be applied to consumers to offset the cost of the increased subsidy. Using diagrams, explain how the size of the lump-sum tax might be calculated using observable information only. Does this leave consumer welfare unchanged? If not, why not?