State the transversality conditions

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Reference no: EM13182727

Consider the house hold problemmax

\(Max c_{t},n_{t},I_{t}b_{t + 1} \) \(E_{t} \sum_{t = 0}^{\infty} \beta^{t}(ln(c_{t} + \theta ln (1 - n_{t}))\)

Such that

\(c_{t} + I_{t} + b_{t + 1} - b_{t} = w_{t}n_{t} + R_{t}k_{t} +r_{t}b_{t} + \pi_{t}.\)

\(k_{t + 1} = I_{t} + (1 - \delta)k_{t}\)

where \(\theta\) is a scalar and all other variables and parameters are as defined in the RBC Class.

.1 State thes implified version of the problem in which the household chooses tomorrow's capital stock instead of today's investment

.2 Given the Setup in 1.1, state the current value Lagrangian.

.3 State the household's first-order conditions for consumption, labor, capital, and bonds

.4 State the transversality conditions

.5 Consider the firm problem

\(Max c_{t},n_{t},I_{t}b_{t + 1} \) \(V_{t} = a_{t}k^{a}_{t}n^{1 - a}_{t} - w_{t}n_{t} - R_{t}k_{t} = \pi_{t}\)

Where \(ln a_{t} + \epsilon_{t}\) and \(a_{t}k^{a}_{t}n^{1 - a}_{t}\) is equal to \(y_{t}\) (the economy's total output). State the firm's first order conditions for labor and capital.

Reference no: EM13182727

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