Consider an RBC model without capital such that the production function is Y = A.Le and...

 

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Consider an RBC model without capital such that the production function is Y₁ = A.Le and the resource constraint is Y = C₁ + Gt. Assume firms are profit maximizing and face a competitive labour market. Assume households maximize expected "lifetime" utility with discount rate p and felicity u₁ = Inc₁ + bln(1 - l), b>0. (a) Write out the analytical expressions for the equilibrium wage in the labour market, the Euler equation, and the first-order condition for . (Hint: in the absence of capital, r = 0.) (b) Solve for the steady state values of wages, output, and consumption given L = 0.2, A = 1, G=0, and b=4. What must the value of p be for a steady state to exist and why? Consider an RBC model without capital such that the production function is Y₁ = A.Le and the resource constraint is Y = C₁ + Gt. Assume firms are profit maximizing and face a competitive labour market. Assume households maximize expected "lifetime" utility with discount rate p and felicity u₁ = Inc₁ + bln(1 - l), b>0. (a) Write out the analytical expressions for the equilibrium wage in the labour market, the Euler equation, and the first-order condition for . (Hint: in the absence of capital, r = 0.) (b) Solve for the steady state values of wages, output, and consumption given L = 0.2, A = 1, G=0, and b=4. What must the value of p be for a steady state to exist and why?

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Answer a The analytical expression for the equilibrium wage in the labour market is w AL the Euler equation is p bAL and the firstorder condition for consumption is u pC bln 1L b The steady state valu... View the full answer