lecture 202-11

# lecture 202-11 - Fall Semester 05-06 Akila Weerapana...

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Fall Semester ’05-’06 Akila Weerapana Lecture 11: Assessing the Solow Model with Technology I. OVERVIEW In the last lecture we looked at the results of some comparative static exercises using the Solow model with technology. We showed that the impact of an increase in the savings rate is identical to the impact in the basic Solow model: there is a short-term increase in the growth rate of per-capita output but in the long run growth is unchanged. In other words, the increase in savings has a level e ff ect, not a growth e ff ect. We also looked at the impact of an increase in the growth rate of technology. The impact of an increase in the growth rate of technology has a growth e ff ect: the steady state growth rate of output and capital per-capita is increased. In today’s class, we will take a closer look at the steady state of the Solow model with technology. We then assess the predictions of the Solow model with technology and think about what avenues remain to be explored. II. COMPARING STEADY STATES We can also do some comparative statics exercises using a little algebra instead of graphs. We know that at the steady state ˙ ˜ k ˜ k = 0. Therefore, using the capital accumulation equation ˙ ˜ k = s ˜ y - ( n + g + δ ) ˜ k we can show 0 = s ˜ y * - ( n + g + δ ) ˜ k * ( n + g + δ ) ˜ k * = s ˜ y * s ˜ k * α = ( n + g + δ ) ˜ k * s n + g + δ = ˜ k * 1 - α ˜ k * = s n + g + δ 1 1 - α Using the fact that ˜ y = ˜ k α we can then show that ˜ y * = s n + g + δ α 1 - α Using the fact that ˜ k = k A and ˜ y = y A we can show that k * t = A t s n + g + δ 1 1 - α and y * t = A t s n + g + δ α 1 - α

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Note that in steady state, k and y are not constant, they are growing over time (hence the subscript t) because technology is growing. Finally, using the fact that k = K L and y = Y L we can show that K * t = A t L t s n + g + δ 1 1 - α and Y * t = A t L t s n + g + δ α 1 - α As is the case with k and y , K and Y are not constant in steady state either, they are growing over time both because technology is growing but also because the population is growing. III. WHAT CAN THE SOLOW MODEL WITH TECHNOLOGY EXPLAIN? Now that we have an idea about the properties of the model, let’s assess the intuitiveness of the predictions of the Solow model with technology. 1. Why are some countries rich and others poor? The Solow model with technology, like the basic Solow model, predicts that countries with high investment (savings) rates, low population growth rates and low rates of capital depre- ciation are likely to have more capital and output per worker.
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