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6. Consider a variation of the Sidrauski monetary model with a constant popu- lation. Specifically, assume that the representative agent's maximize lifetime utility is given by: [s [ u (a)+ v ( 14 ) ] where U (.) and V (.) are concave, twice-differentiable functions, c (t) denotes consumption and M (t) is money chosen in period t. Each period, agents use beginning of period nominal balances, the revenue from sales of output and a lump-sum monetary transfer to purchase consumption, investment and new money. In contrast to the Sidrauski model, both capital and money are used as inputs into the production process. Letting y denote output, the production function is given by: where =' (.) 0, = (0) = 1, lim = (M/P) = 0. The function f (k;) has standard properties. The money supply in this economy is growing at the constant rate / > 0 and capital depreciates at the constant rate of 6