Consider a one-period economy with a single representative consumer, a single representative firm and the government. The representative consumer derives utility from consumption c and leisure l:

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

The firm produces output Y using capital K and labor N according to

Y = zK^a N^1-a

where z is the total factor productivity and a is the Cobb-Douglas parameter. The firm maximizes profits which are then transferred to the representative consumer.

The government balances the budget using lump-sum taxes T on the representative consumer to finance government spending G. The hourly wage in this economy is w and the consumer has h hours to divide between leisure and labor.

Write down the consumer's budget constraint and the firm's profits function. (Provide a detailed answer)