In an economy where inflation is costly and price setting firms are monopolist- ically competitive, national income is defined as follows: Mt = C+ + Output, y equals the sum of consumption expenditure, G, and the costs as- sociated with changes in inflation, *. Goods are produced using a production function that is linear in labour: Mt = n where n denotes hours worked. Inflation in this model evolves according to a new Keynesian Phillips curve: Nt = Butt1 + (E - 1 ) (emct - 1) 3/t where me denotes the firm's marginal costs and the parameter 1. The marginal costs of the firm are defined as: me = Wt where wy is the real wage. From the household's optimisation problem, we know that the marginal rate of substitution between hours and consumption equals the real wage: Unit = wt- 1. What is the optimal monetary policy for this model? Carefully explain why the monetary authority needs a 'helping hand' from fiscal policy to implement this policy. 2. Assuming that the utility function of the household takes the following form: Ut = In (ct - n/ ) work out the effect of the 'helping hand' of fiscal policy on the supply of la- bour. Explain why this helps to offset the effects of monopolistic competi- tion