8.23.      The following is known as the transcendental production function (TPF), a generalization of the well-known Cobb–Douglas production function:

Yi  = β1 Lβ2 kβ3 eβ4 L+β5 K

where Y = output, L = labor input, and K = capital input.

After taking logarithms and adding the stochastic disturbance term, we obtain the stochastic TPF as

ln Yi   = β0 + β2 ln Li + β3 ln Ki  + β4 Li + β5 Ki  + ui

where β0 = ln β1 .

a.    What are the properties of this function?

b.     For the TPF to reduce to the Cobb–Douglas production function, what must be the values of β4 and β5?

c.     If you had the data, how would you go about finding out whether the TPF reduces to the Cobb–Douglas production function? What testing procedure would you use?

d.     See if the TPF fits the data given in Table 8.8. Show your calculations.