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

U = u (c, l) = ln (c) + ln (l)

where c is consumption and l is 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. (Provide detailed answers for the following parts)

a) Write down Ina's budget constraint.

b) 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?

c) 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?

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

e) Given the answer in the previous section, why do countries prefer to tax labor income instead of a lump sum tax?