The production function q = KaLb, where “a” and “b” are both between 0 and 1, is called a Cobb-Douglas production function. It is widely used in economic research because with different value of “a” and “b” we can model a variety of production processes.
a. Show that the production function q = *KL is a special case of the Cobb- Douglas production function.
b. Show that with a Cobb-Douglas production function, if a + b = 1, it means a doubling of K and L will double output q.
c. If a + b < 1, will a doubling of K and L also double the output q, or will the output be more than or less than double? What kind of returns to scale would this reflect?