Kent State University Macroeconomic Theory I Practice February 27, 2014 Consider a static economy with 2 consumption goods and labor. The government needs to “consume” g = (g1 , g2 ) = (3, 4). That is, it needs to purchase 3 units of good 1 and 4 units of good 2. In order to fund its expenditure, the government has available linear taxes on consumption goods τ1 and τ2 . The representative household solves (normalizing w = 1) max α1 ln(c1 ) + α2 ln(c2 ) − l (c1 ,c2 ,l) s.t. (1 + τ1 )p1 c1 + (1 + τ2 )p2 c2 = l where ci is the consumption of the good i = 1, 2, and l is labor. The representative firm solves max p1 y1 + p2 y2 − l (y1 ,y2 ,l) s.t. y1 y2 + =l θ1 θ2 where yi is the output of good i = 1, 2. a. Set up the Ramsey problem for this economy. b. Now suppose parameters for this economy are given by (α1 , α2 , θ1 , θ2 ) = (0.3, 0.7, 12, 18). Solve the Ramsey problem for those particular values of parameters. The rest of this question is about the implementation of the optimal allocation that you just found. c. Characterize the firm’s solution and the consumer’s solution. d. How should taxes be set in this economy? In other words, find the consumption taxes τ1 and τ2 that implement the optimal allocation. e.Verify that the government’s budget constraint is satisfied. 1