For the CobbDouglas production function given in Example 4.5, use A = 20, = 0.7, and = 0.5. Answer the following: a. What

For the Cobb–Douglas production function given in Example 4.5, use A = 20, α = 0.7, and β = 0.5. Answer the following:

a. What can you say about the returns to scale?

b. What is the output and elasticity if both inputs equal 20?

c. What is the rate of technical substitute at that same point?

Example 4.5 Consider the following production function (known as Cobb–Douglas):

Figure 4.4 shows the input possibility set and isoquant when α = β = 0.5, A = 10, and y = 20. We can determine the returns to scale as follows:

Therefore, it exhibits CRS. Note that it is easy to see that, whenever α + β = 1, Cobb–Douglas is CRS. The RTS when α = β = 0.5 and A = 10 is equal to

FIGURE 4.4:

f(x)=y=Axix.