Assume an economy where households receive utility from consumption of goods and leisure. u: = in (ct mo?) Households maximise utility subject to the fol- Itiwing intertemporal budget constraint: PtCt + Pill-B: + Mt + 5:3: = Pttht + Mtl + Btl + {5: + Dt}atl Where Pic: is nominal consumption, FF is the price of bonds, Bt is the level of bond holdings. 5: is the share price, at the stock of shares purchased by the household in period t. D; is a dividend payment and M; is the money stock held by agents at the end of period t. win: denotes the household's labour income. In addition to the flovv budget constraint, the household also faces a cash-inadvance constraint: PtCt = Mt (a) Set up the intertemporal Lagrangian and derive the first-order conditions with respect to ct. at. B: and Mr. [5 marks} (b) Show how the presence of a cash-in-advance constraint distorts the consumption-labour decision. (1' marks) {c} Show and explain how the labour supply responds to an increase in the nominal interest rate [keeping all other variables constant]. [T marks] (d) What does Friedman's monetary policy rule imply and hovv can it be used to eliminate the distortions in the model that arise from the cash-in-advance assumption? [14 marks)