Random matching and money in the neoclassical growth model: some analytical results

I use the monetary version of the neoclassical growth model developed by Aruoba, Waller and Wright (2008) to study the properties of the model when there is exogenous growth. I first consider the planner's problem, then the equilibrium outcome in a monetary economy. I do so by first using proportional bargaining to determine the terms of trade and then consider competitive price taking. I obtain closed form solutions for the balanced growth path of all variables in all cases. I then derive closed form solutions for the transition paths under the assumption of full depreciation and, in the monetary economy, a non-stationary interest rate policy.