I need help with this question please

Consider a oneperiod economy with a single representative consumer, a sin gle representative rm and the government. The representative consumer derives utility from consumption c and leisure l: u[c,l)=inc+lnl (1) The rm produces output Y using capital K and labor N according to Y = zKaNl'\" (2) where z is the total factor productivity and a is the CobbDouglas parameter. The rm maximizes prots :Ir which are then transferred to the representative consumer. The government balances the budget using lump-sum taxes T on the repre sentative oonsumer to nance government spending 6". The hourly wage in this economy is a: and the consumer has n hours to divide between leisure and labor. (i) Write down the consumer's budget constraint and the rm's prots function. {05 marks) (ii) Assume that m = 10, z = 20+ a = 0.3? and K = 1. Calculate the number of hours that the rm would like to hire and the prots of the representative rm. (05 marks) (iii) Assume that government spending G is 10I the representative consumer receives the prots that you caiculated above and earns hourly wage to = 10. Calculate how many hours of work the representative eon sumer would like to supply in the market. (ID marks) (iv) In the economy described above. (i) the government budget is balanced, (ii) the representative consumer maximises lifetime utility given the budget constraint and m, and (iii) the rm maximizes prots given the production function and in. Is this a competitive equilibrium? 'Nhy or why not? {05 marks) Total: 25 marks