Question 1 Consider a one-period economy with a single representative consumer, a sin- gle representative rm and the government. The representative consumer derives utility from consumption 0 and leisure l: u(c,l)=lnc+lnl (1) The rm produces output Y using capital K and labor N according to Y = zKa'N1_\"' (2) where z is the total factor productivity and a is the Cobb-Douglas parameter. The rm maximizes prots 7r which are then transferred to the representative consumer. The government balances the budget using lump-sum taxes T on the repre- sentative consumer to nance government spending G. The hourly wage in this economy is w and the consumer has It 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 w = 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 10, the representative consumer receives the prots that you calculated above and earns hourly wage w : 10. Calculate how many hours of work the representative con- sumer would like to supply in the market. (10 marks) iv In the economy described above, i the overnment bud et is balanced, g E; (ii) the representative consumer maximizes lifetime utility given the budget constraint and w, and (iii) the rm maximizes prots given the production function and 11). Is this a competitive equilibrium? Why or why not? (05 marks) Total: 25 marks