Exercise Set 9
ECONOMIC GROWTH

I. Objectives

1. To understand diminishing returns to capital
2. To analyze sources of economic growth

II. Data

Consider the aggregate production function, y = Ak^0.6, where y is real GDP per worker (or productivity), A is level of technology, and k is (physical) capital per worker. The technology level (A) is also referred to as  total factor productivity (TFP). When TFP increases, the economy can produce more output with the same quantity of physical capital, human capital, and labor. TFP is is considered central to economic growth. (Note: In the current problem, we ignore human capital, focusing instead on physical capital.)

III. Questions

1. Sketch the aggregate production function, with k on the horizontal axis and y on the vertical axis.
2. From the graph above, we conclude that as capital per worker increases, ceteris paribus, output per worker will increase at [ an increasing rate | a constant rate | a decreasing rate ].
3. Compute the GDP per worker for the following values of k:
1. k = 60:     y₆₀ = __________
2. k = 90:     y₉₀ = __________
3. k = 120:   y₁₂₀ = __________
4. Compute the differences:
1. y₉₀ - y₆₀ = ______________
2. y₁₂₀ - y₉₀ = ______________
5. Consider your answers in Q. 3 and Q.4. In Q.3 we increased k by the same amount (30) from (a) to (b), and then (b) to (c). In Q.4 we obtained the corresponding increases in output per worker. Do these calculations reflect diminishing returns to physical capital?
6. Consider an improvement in technology. This is captured by an increase in the parameter A. Suppose A increases to 15.
1. Sketch the new production function on the same graph in Q. 1.  
2. We note from the graph that, at a given value of k, the value of y is now [ greater | smaller | unchanged ].