Econ303 Homework 8: Household Budget Constraint and Savings with Taxes and Social Security, Assignments of Macroeconomics

Download Econ303 Homework 8: Household Budget Constraint and Savings with Taxes and Social Security and more Assignments Macroeconomics in PDF only on Docsity! Econ303 Homework 8 Answer 1 Household life-time utility is √ c1 + 0.9 √ c2 MRS between c2 and c1 = 0.9MUc(2) MUc(1) = 0.9 1 2 √ c2 1 2 √ c1 = 0.9 √ c1√ c2 The real interest rate r = 10%. Income of household y1 = 50, 000 and y2 = 20, 000. 1. 1.5 points Without government, household budget constraint is c1 + c2 1 + 0.1 = 50000 + 20000 1 + 0.1 Household marginal condition is MRS between c2 and c1 = 1 1 + r That is 0.9 √ c1√ c2 = 1 1 + 0.1 Square the both sides 0.92c1 c2 = 1 (1 + 0.1)2 c2 = 0.9 2 · (1 + 0.1)2 · c1 Substitute into household budget constraint, we have c1 + 0.92 · (1 + 0.1)2 · c1 1 + 0.1 = 50000 + 20000 1 + 0.1 [1 + 0.92 · (1 + 0.1)]c1 = 50000 + 20000 1 + 0.1 c1 = 50000 + 20000 1+0.1 1 + 0.92 · (1 + 0.1) = 36056 c2 = 0.9 2 · (1 + 0.1)2 · c1 = 35338 Household saving y1 − c1 = 50000− 36056 = 13944 2. 1.5 points When household subjective discount factor increases to 0.95, MRS between c2 and c1 = 0.95MUc(2) MUc(1) = 0.95 √ c1√ c2 Econ303 Homework 8 Answer 2 Household marginal condition is 0.95 √ c1√ c2 = 1 1 + 0.1 Square the both sides 0.952c1 c2 = 1 (1 + 0.1)2 c2 = 0.95 2 · (1 + 0.1)2 · c1 Substitute into household budget constraint, we have c1 + 0.952 · (1 + 0.1)2 · c1 1 + 0.1 = 50000 + 20000 1 + 0.1 [1 + 0.952 · (1 + 0.1)]c1 = 50000 + 20000 1 + 0.1 c1 = 50000 + 20000 1+0.1 1 + 0.952 · (1 + 0.1) = 34215 c2 = 0.95 2 · (1 + 0.1)2 · c1 = 37364 Household saving y1−c1 = 50000−34215 = 15785. When household cares more about future, household saves more. 3. 2 points When government levies capital income tax of 50%, household budget con- straint becomes c1 + c2 1 + 0.05 = 50000 + 20000 1 + 0.05 Household marginal condition becomes MRS between c2 and c1 = 1 1 + (1− τ)r That is 0.9 √ c1√ c2 = 1 1 + 0.05 Square the both sides 0.92c1 c2 = 1 (1 + 0.05)2 c2 = 0.9 2 · (1 + 0.05)2 · c1 Substitute into household budget constraint, we have c1 + 0.92 · (1 + 0.05)2 · c1 1 + 0.05 = 50000 + 20000 1 + 0.05