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A Simple Representative Agent Model

A Simple Representative Agent Model. Dr. Kai Sun. A simple representative agent model. Specify preferences, endowments, and technology Obtain optimal solution and equilibrium. A simple representative agent model. N consumers (they consume only one good) and no money (barter economy)

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A Simple Representative Agent Model

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  1. A Simple Representative Agent Model Dr. Kai Sun

  2. A simple representative agent model • Specify preferences, endowments, and technology • Obtain optimal solution and equilibrium

  3. A simple representative agent model • N consumers (they consume only one good) and no money (barter economy) • Utility function: U(c,l) • c: consumption • l: leisure • U(.) is strictly decreasing, strictly convex, and twice differentiable • Draw the U(.) and explain marginal utility

  4. A simple representative agent model • Initial capital: K0/N for each person • K0 is total capital • Each person has 1 unit of time: l+n=1 • n is labor • M firms, and each firm has a production function: y=z‧f(k,n) • z: technology parameter

  5. More about the production function • f(k,n) is: • Strictly increasing in k and n • Strictly quasiconcave • Twice differentiable • Homogeneous of degree (H.O.D.) 1 in inputs • Constant Returns to Scale (CRS) • Example: f(k,n)=k+n • All markets are competitive.

  6. Optimization for a representative consumer • st. • consumption = wage income + capital income • Consumers consume everything they get. • r: rental rate of capital • w: wage rate • ks: capital supply, and • Consumers supply all the capitals: • numeraire: consumption goods (i.e., price of the consumption goods = 1)

  7. Optimization for a representative firm • k=ks • Price of output=price of consumption good=1 • Profit = total revenue – total cost

  8. Competitive Equilibrium (C.E.) • A C.E. is a set of quantities: c, l, n, k and a set of prices: w, r (given) • st. • Each consumer chooses c and l optimally. • The firm chooses n and k optimally. • All markets clear. • Labor market • Goods market • Capital market

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