Problem Set 3

Econ W3213

Intermediate Macroeconomics

Spring 2013

Due at the beginning of class Thursday March 7th

(or in mailbox 20 in IAB 1022 before that point)

1. Answer exercises 5 and 7 at the end of chapter 5 of Jones. Note that these problems are meant

to be answered using the Solow model

.

2. The Harrod-Domar model (aka Surplus labor model). Consider an economy in which

labor is not a scarce resource and therefore it is possible to double production by doubling the

capital stock.

a) Suppose production is a function of both capital and TFP ̅. Given the assumption made

above, what functional form must the production function take?

b) Suppose the savings rate is ̅, the production function is as in part (a) and the capital

accumulation equation is the same as in the Solow model:

̅

Plot investment and depreciation as a function of capital. Use the graph to explain why the

Harrod-Domar model has no steady state.

c) Suppose ̅ 10, ̅ 1 and ̅ 10. What is the growth rate of this economy?

d) Suppose the World Bank would like to increase the growth rate of this economy to 7%. How

could it do this?

3. Solow model with TFP growth but no population growth. Consider a Solow model in

which there is steady growth in TFP but no growth in the population. TFP growth is given by

1

The production function in the economy is

/ /

Capital accumulation is given by

̅ ̅

a) Rewrite the equations of the model in terms of output and capital per effective worker:

and

where

/

.

b) Draw a Solow diagram for this economy and describe the steady state.

c) What is the growth rate of output per capita in the steady state?

d) Suppose the economy begins with a capital stock per effective worker that is lower than the

steady state. Describe the transition dynamics using a Solow diagram. Plot time series plots for

output per effective worker and for the level of output (see figure 5.7b for an example of a time

series plot).

e) Derive the steady state level of capital per effective worker and the steady state level of output

per effective worker mathematically.

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