Dear Expert Tutors,

Please help me solve the following problem with a model with exogenous government expenditures.

Consider the following innite horizon economy. The representative household maximizes period utility Mat, 1;) = ].n[ct) +131; where at and It are period consumption and leisure. The household is endowed with a unit of time each period which is spread across leisure and labour, nt. Time is discounted by a subjective discount factor J3 E (U, 1]. There is no capital and households can trade oneperiod bonds with each other. Let Q; be the period t price of a [noncontingent) bond that returns one unit of the consumption good in period t + 1. End of period t holdings of bonds is denoted by 3):. Households are subject to a NowPonziGames conditions that - T hmTaoo (11:0 qt) hr = 0. There is a representative rm that buys labour services from the representative household at the competitive wage, to: and is owned by the household. The rm pro duces a nal good from labour using a linear production technologyr y; = 2m. There is also a government that nances a stochastic stream of government expenditures via a linear labour income tax at rate 11. In other words, each period, the government nances its expenditure, gt, by levying a tax on the representative household's labour income such that each period the government runs a balanced budget. Let gt follow a known stochastic process with g; E [2,]. Assume that z > {E and \"q 6 {0T 1)