Solve it plzzzz

Consider an economy where production technology is augmented by public investment: 3; = F [G,N ) = GEN 1\". In that sense, the government expenditure is not wasteful anymore and it increases the eicierrcy of production in the private sector (you can actually prove that it increases the marginal product of labor at each production level). Suppose the government investment can be nanced by lump-sum tax levied on the consumer: G = T. The consumer's side is the same as before and his] her preference is in GHH form. 1. Given there is no distortion in this economy, we consider the social planner's problem who maximize the consumer's utilityr subject to recourse constraint. Assume the public investment is exogenous, which cannot be controlled by the social planner. Solve the social planner's problem. (Hint: the resource constraint is c + G = GQ'N 10} 2. Analyze the effect of an increase in government expenditure on equilibrium prices and quan- tities (wage, output, consumption, and hours worked). Draw appropriate graphs to illustrate. 3. We know in class that the wasteful government spending generates crowding-out eect in our one-period model. Does the crowding-out get smaller or bigger in this economy when the government spending is productive