Consider a representative agent with the utility function U = E [0 [[(C+i) (1 Bi +1)...
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Consider a representative agent with the utility function U = E₁ [₁²0 [[(C₁+i) (1 Bi +1) ² (1 = Next) 1-7 − Nt+i) ¹-p]¹- a Where is the relative risk aversion coefficient. The production function it's Cobb- Douglas function, represented by Y₁ = (A₁N₁)"K!-" _and the equation of motion of capital is K+1 = (1 − 8)K₂ + Y₁ - C₁, where is the depreciation rate. a. Write down the optimization problem for the agent in this setup. Hint: Define the state and controls variables and write the Bellman equation. b. Using this specification of production, derive the first order optimality conditions for the optimal choices of A,, N, and K₁+1 Consider a representative agent with the utility function U = E₁ [₁²0 [[(C₁+i) (1 Bi +1) ² (1 = Next) 1-7 − Nt+i) ¹-p]¹- a Where is the relative risk aversion coefficient. The production function it's Cobb- Douglas function, represented by Y₁ = (A₁N₁)"K!-" _and the equation of motion of capital is K+1 = (1 − 8)K₂ + Y₁ - C₁, where is the depreciation rate. a. Write down the optimization problem for the agent in this setup. Hint: Define the state and controls variables and write the Bellman equation. b. Using this specification of production, derive the first order optimality conditions for the optimal choices of A,, N, and K₁+1
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Related Book For
Microeconomics An Intuitive Approach with Calculus
ISBN: 978-0538453257
1st edition
Authors: Thomas Nechyba
Posted Date:
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