Please help me to solve this question :

Suppose Ina, the representative consumer, derives utility from consumption and leisure with the following utility function:

U=u(c,l)=lnc+lnl

wherecis consumption andlis leisure. She has 16 hours per day to allocate between leisure and work and earns a wage of$10 dollars per hour. She owns shares of an index fund that includes all the firms in Canada and earns$15 dollars per day on average as profits. In addition she pays a lump sum tax of$5 per day

(i) Write down Ina's budget constraint.

(ii) She has a choice to work either part-time (4 hours per day) or full-time (8 hours per day). Is either of these choices optimal? How many hours would she choose if she was free to choose her working hours?

(iii) A new government is elected and replaces the lump sum tax with a 7% flat rate on labor income= 0.07. If she is free to choose her working hours, what is the optimal amount of working hours?

(iv) Compare the government revenues with the lump sum and labor income tax. What happens to labor supply and consumption?

(v) Given your answer in the previous section, why do you think countries prefer to tax labor income instead of a lump sum tax?