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 (1)

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

Y = zK^aN^1a (2)

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.

1. Assume that government spending G is 10, the representative consumer receives the profits that you calculated above and earns hourly wage w = 10. Calculate how many hours of work the representative consumer would like to supply in the market.

Assume that w = 10, z = 20, a = 0.3, and K = 1.