1. Consider the production function f(x1, x2) = x21 x22 . Does this exhibit constant, increasing, or decreasing returns to scale?
2. Consider the production function f(x1, x2) = 4x121 x132 . Does this exhibit constant, increasing, or decreasing returns to scale?
3. The Cobb-Douglas production function is given by f(x1, x2) = Axa1xb2.It turns out that the type of returns to scale of this function will depend on the magnitude of a + b. Which values of a + b will be associated with the different kinds of returns to scale?
4. The technical rate of substitution between factors x2 and x1 is -4. If you desire to produce the same amount of output but cut your use of x1by 3 units, how many more units of x2 will you need?