Econ. 153a 
Fall 1996 
C. Sims 
Due Wednesday, 11/6. You may collaborate with other students, provided that you write up answers yourself and identify people you have worked with. These questions are meant to resemble what might go on a final exam, though some of them may take a little longer to answer than would real exam questions. To get the most benefit, you should probably work at the questions on your own first, before consulting with others. The point scores on this exercise will make up 10% of the overall course grade.
1. What are the implications of the standard Solow growth model with CobbDouglas technology when ? Is there a steady state value of k? Does the growth rate converge to some limiting value as ?
2. Consider the Solow model with a CES production function, i.e. with
(1) 
In this production function we require and , with producing the CobbDouglas special case. An interesting fact is that when , not every set of values for the other parameters s,a , n, A, and implies the existence of a steady state with constant .
[Note that the answers to these two questions may be different according to whether or .]
3. In the Solow model with CES production function we can introduce purely laboraugmenting technical change and still possibly find a steadystate. (We know this because it is true with any linear homogenous production function in the Solow model.) That is, we can replace L in with , and possibly find that the model converges to a steady state in which is constant, under the usual assumption of exogenous population growth at the rate n. On the other hand, this is not in general true if instead we have capitalaugmenting technical change, i.e. we replace K in with
.
4. Consider a twoperiod life OG model with a distorting tax on capital. That is, we assume as usual that consumers born at t maximize
subject to
.
The tax is paid by consumers, so the price paid for capital by firms, Q, is still 1+r, despite the existence of the tax. The parameter g is a per capita transfer payment to the young, financed out of the tax on capital. The government budget constraint is
.
Assume the capital tax rate is fixed at and (as usual) that population grows at the constant rate . Assume also that firms use a CobbDouglas technology:
.
5. The Solow model is traditionally presented in continuous time. A discrete time version would make the following changes in the equations
Continuous Time 
Discrete Time 




Can you derive an expression for steady state capital stock and output per worker in the discrete time version? Does it depend on parameters in the same way as the corresponding continuous time expression?
6. The Solow model assumes a constant rate of savings out of gross output (including depreciation). In the OG model, the savings rate out of gross output varies systematically with the parameters of the model.
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