Consider the following economy populated by a government and a representative household. There is no uncertainty and the economy and the representative household and government within it last forever. The government consumes a constant amount gt = g > 0, t ≥ 0. The government also sets sequences of two types of taxes, {τct, τkt}∞t=0 . Here τct, τkt are, respectively, a possibly time-varying flat rate tax on consumption and a time varying flat rate tax on earnings from capital. The preferences of the household are ordered by Where β ∈ (0, 1) and u(·) is strictly concave, increasing and twice continuously differentiable. The feasibility condition in the economy is Where kt is the stock of capital owned by the household at the beginning of time t and δ ∈ (0, 1) is a depreciation rate. At time 0, there are complete markets for dated commodities. The household faces the budget constraint: Where we assume that the household inelastically supplies one unit of labor, and qt is the price of date t consumption goods, rt is the rental rate of date t capital, and wt is the wage rate of date t labor. A production firm rents labor and capital. The value of the firm is Where here kt is the firm’s capital-labor ratio and nt is the amount of labor it hires. The government sets {gt} exogenously and must set the sequences {τct, τkt} to satisfy the budget constraint: a. Define a competitive equilibrium. b. Assume an initial situation in which from time t ≥ 0 onward, the government finances a constant stream of expenditures gt = g entirely by levying a constant tax rate τk on capital and a zero consumption tax. Tell how to find steady state levels of capital, consumption, and the rate of return on capital. c. Let k0 be the steady value of kt that you found in part (b). Let this be the initial value of capital at time t = 0 and consider the following experiment. Suddenly and unexpectedly, a new party comes into power that repeals the tax on capital, sets τk = 0 forever, and finances the same constant level of g with a flat rate tax on consumption. Tell what happens to the new steady state values of capital, consumption, and the return on capital. d. Someone recommends comparing the two alternative policies of (1) relying completely on the taxation of capital as in the initial equilibrium and (2) relying completely on the consumption tax, as in our second equilibrium, by comparing the discounted utilities of consumption in steady state, i.e., by comparing 1 1−β u(c) in the two equilibria, where c is the steady state value of consumption. Is this a good way to measure the costs or gains of one policy vis a vis the other?
Consider the following economy populated by a government and a representative household. There is no uncertainty and the economy and the representative household and government within it last forever. The government consumes a constant amount gt = g > 0, t ≥ 0. The government also sets sequences of two types of taxes, {τct, τkt}∞t=0 . Here τct, τkt are, respectively, a possibly time-varying flat rate tax on consumption and a time varying flat rate tax on earnings from capital. The preferences of the household are ordered by
Where β ∈ (0, 1) and u(·) is strictly concave, increasing and twice continuously differentiable. The feasibility condition in the economy is
Where kt is the stock of capital owned by the household at the beginning of time t and δ ∈ (0, 1) is a
Where we assume that the household inelastically supplies one unit of labor, and qt is the price of date t consumption goods, rt is the rental rate of date t capital, and wt is the wage rate of date t labor. A production firm rents labor and capital. The value of the firm is
Where here kt is the firm’s capital-labor ratio and nt is the amount of labor it hires. The government sets {gt} exogenously and must set the sequences {τct, τkt} to satisfy the budget constraint:
a. Define a competitive equilibrium.
b. Assume an initial situation in which from time t ≥ 0 onward, the government finances a constant stream of expenditures gt = g entirely by levying a constant tax rate τk on capital and a zero consumption tax. Tell how to find steady state levels of capital, consumption, and the
c. Let k0 be the steady value of kt that you found in part (b). Let this be the initial value of capital at time t = 0 and consider the following experiment. Suddenly and unexpectedly, a new party comes into power that repeals the tax on capital, sets τk = 0 forever, and finances the same constant level of g with a flat rate tax on consumption. Tell what happens to the new steady state values of capital, consumption, and the return on capital.
d. Someone recommends comparing the two alternative policies of (1) relying completely on the
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