Consider a one-period economy with a single representative consumer, a sin- gle representative firm and the government. The representative consumer derives utility from consumption c and leisure l: u(cl) = Inc+Inl (1) The firm produces output Y using capital K and labor N according to Y = 2KN1-a (2) where z is the total factor productivity and a is the Cobb-Douglas parameter. The firm maximizes profits a which are then transferred to the representative consumer. The government balances the budget using lump-sum taxes T on the repre- sentative 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. b=16 (i) Write down the consumer's budget constraint and the firm's profits function. (05 marks) (ii) Assume that w = 10, z 20, a 0.3, and K = 1. Calculate the number of hours that the firm would like to hire and the profits of the representative firm. (05 marks)