Our theory indicates that over time society has generated national income from c

Question

Our theory indicates that over time society has generated national income from capital and labor at a fairly constant rate which has led to the development of the Cobb-Douglas production function. Assume society has an initial allocation of 36 laborers and 49 units of capital with a technology level that doubles production. In homework 7 we proved that when capital and labor provide an even share of output (i.e an alpha of 0.5) constant returns to scale existed. What if the share of labor becomes 70% (a more realistic value), does the function still exhibit constant returns to scale, mathematically prove your answer with the above input values

Explanation / Answer

If the share of labor becomes 70%, it implies marginally an incease in one unit of labor will increase 70% more in the productivity of labor. Hence this is not a case of constant rturn but a case of increasing return to scale.

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