I have been stuck on this question for about two days and can find no way out (apologies if the question seems really simple as I haven't started university yet). I would strongly prefer it if this can be solved using the Lagrange multiplier. Thanks.
There are two individuals, A and B, in an economy. Each derives utility from his consumption, C, and the fraction of his time spent on leisure, l, according to the utility function: U = ln(C) + ln(l) However, A is made very unhappy if B’s consumption falls below 1 unit, and he makes a transfer, G, to ensure that it does not. B has no concern for A. A faces a wage rate of 10 per period, and B a wage rate of 1 per period. (a) For what fraction of the time does each work, and how large is the transfer G?