first assume the firm face competitive market in both input and output markets.
also, let the production function be Xt=MtF(nt), while X is output, M is productivity, n is input, t is time subscrib.
further suppose that we have a learning-by-doing effect, so that we have another condition as: Mt+1 - Mt = dMtF(nt).
assume there is a constant interest rate r.
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