Production Function

Consider the Solow model with no technological progress. Suppose the rate of population growth is 0.02 and the depreciation rate is 0.08. Suppose the economy’s production function is y =4k0.5, and its saving rate is 0.20.

A. Find the steady state values of capital per worker (k), output per worker (y) and consumption per worker (c). (6 points).

B. If there were exogenous technological change at the rate of g=0.03, what would the steady state behaviour of y and k be? Demonstrate. (6 points)

Question 3 (8 points)

According to demographers, population growth in countries like Canada will fall to zero later this century. Explain the transitional and steady state effects on the output per person and its growth rate in the Solow model with no technological change. Draw a graph to support your answer.

Question 4 (12 points)

A. According to the Solow model without technological change, poor countries will grow faster than rich countries, and would, therefore, converge to the same output per person in the long run. Explain why with the help of a graph.
(4 points)

B. The Excel file convergence.xlsx contains data on output per person in 1980 (y1980) in 2011 US dollars and the average growth rate of output person (gy) over the 1980-2015 interval for developing countries whose 1980 output per person was less than S10,000. The data file is on Brightspace.

1. What is output per person in 1980 in the richest country and the poorest country in the sample? How do these countries compare in terms of growth rates? (2 points)

2. Present a graph that plots the average growth rate of output per person over the 1980-2015 interval (gy) against 1980 output person (y1980). Explain what you would expect the graph to show if the Solow predictions in A. above are valid? Are those predictions borne out by the data? Explain briefly. (6 points)