Suppose the government introduces a tax on the consumer's capital income, ?k , and a lumpsum transfer, T, which goes back to the consumer. Show and explain how the constraints presented above change. Write down and explain the government budget constraint. Discuss the effect on the equilibrium gross interest rate, (1+r), and capital at time 1, k1, from introducing this tax.

Consider the following description of preferences constraints and production respectively for a two- psriod decentralised economy: at = lnicfi'l + :3 Inc-i) Cg =}'D_k$l cf=sl+kifl+r} IIEET=AkaJE where u is discounted lifetime utility: in is the natural logarithm: :3 and of refer to consumption demand in time periods [f and 1; El s: l3 s: l is a fixed parameter: ya :1:- {l [fixed parameter} and y] radar to output in time periods {i and l; s] is profits in time period 1; is} is the supply of the capital stock at the start of time period 1; r is the net interest rate: A :r [f is a fixed parameter: k',' is the capital demand of the firm: and {i s: o: c: i is a fixed parameter