Question

1. draw a graph of a production function for per capita income

2. how is the shape of the graph related to convergence

3. how does technology effect p.f.

Answer 1

1.Generally speaking Production function is the technological relationship between the different factors of production and the Output. Per Capita production function is obtained when we divide the production function with L(labour) on both sides. It can be drawn graphically as-

The curve PF/L is the Production function per capita, which shows the level of per capita GDP against per capita Capital.

2.Convergence is a theoretical concept which says that eventually the lower per capita Income Countries will catch up with the higher per capita income countries some day.

It can be also understood from the graph. The main reason for the development of the higher income countries is the availability of higher per capita capital which increases per capita income. But it can be seen from the graph that as there is increase in per capita capital, the increase in per capita income is smaller. As can be seen from the size of triangles in above figure.

3.Technology is one of the most important component of the production function. Let's take example of Cobb-Douglas production function.

So, as the technology improves, the production function improves and there are higher yields.

It can be seen from the graph below, as technology improves and value of A changes, then there is shift in the production function upwards to PF1 and PF2. Which gives higher per capita GDP.