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Question: consider a two period model inhabited by a continuum of...

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Consider a two period model inhabited by a continuum of households on the unit interval and a single representative firm.(In other words treat this as a problem with one agent and one firm). The households live for two periods and then die and wish to maximize their lifetime utility which is given as: The individual buys the consumption good c from the firm at a price of one and sells its labor in each period, nt, at wage wt. In addition the household is able to buy and sell bonds, b, with other households in period one at a price of 1 and receives (1+) in interest from its holdings in period two. The household also owns the firm from which it receives profits π, as dividends. The household takes the profits of the firm and the wage rate as given. The representative firm, buys labor ng in the labor market from the household and produces output with production function f(n2)-Adnf), for A > 0 and α ε (0, 1). (a) Define the competitive equilibrium of the economy (b) Write out the households period by period budget constraint, combine these into a lifetime budget constraint. How does this compare to the budget constraint in the social planners problem:? (c) Set up the Lagrangian for the households problem (d) Obtain and interpret the optimality conditions (e) Find the solution to ci,ni, n2 and c. You may leave these in terms of the prices r and w Tt-

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