1. An economy comprises of a consolidated household sector, a firm sector and the gov- ernment. The household supplies labour (L) to the firm. The firm produces a single good (Y) by means of a production function Y = F (L), F' (L) > 0, F" (L) < 0, and maximizes profits II = PY – WL, where P is the price of Y and W is the wage rate. The household, besides earning wages, is also entitled to the profits of the firm. The household maximizes utility (U), given by U = }In C + In () – a (L), where C is consumption of the good and is real balance holding. The term d (L) de- notes the disutility from supplying labour with d' (L) > 0, d" (L) > 0. The household's budget constraint is given by: PC + M = WL +II+ M – PT, where M is the money holding the household begins with, M is the holding they end up with and T is the real taxes levied by the government. The government's demand for the good is given by G. The government's budget constraint is given by: M – M = PG – PT. Goods market clearing implies Y =C +G. Prove that * € (0, 1), and that government expenditure crowds out private consumption (i.e., E< 0). (b) Show that everything else remaining the same, a rise in M leads to an equipro- portionate rise in P.