The Diamond Overlapping-generations Model a) Assume that the utility function of the representative agent is logarithmic

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The Diamond Overlapping Generations Model A Assume That The Utility Function Of The Representative Agent Is Logarithmic 1 (175.34 KiB) Viewed 33 times

The Diamond Overlapping-generations Model a) Assume that the utility function of the representative agent is logarithmic, that is, the utility in any period is InCt and has a subjective discount rate of 0.1, lives two periods and works in the first one. Write the Lagrange faced by the individual seeking to maximize his inter-temporal utility subject to the present value of consumption being equal to his income. Find Euler's equation, the consumption function when young, and the saving rate for young people. b) Assume that the production function is Cobb-Douglas of the type Yt = 2Kt^0.4 (AtLt)^0.6. The labor force grows at 0.02 and the technology grows at 0.01, while the depreciation rate is 0. Obtain the equation that describes the evolution of kt+1 as a function of k, make the diagram and find the value of k in the stationary equilibrium both analytically and graphically. Describe how an increase in the job growth rate from 0.01 to 0.02 affects kt+1 as a function of kt and the steady state equilibrium. c) Find the path of capital per effective unit in the transitional dynamics of the model specified in the original problem. d) Redo the previous two parts, but now assume a discretionary drop (e.g., a war) in the entire production function, which is now equal to Yt = 1.8Kt^0.4 (AtLt)^0.6 =