12.58 You have been asked to develop an exponential production function—Cobb-Douglas form—that will predict the number of microprocessors produced by a manufacturer, Y, as a function of the units of capital, X1; the units of labor, X2; and the number of computer science staff involved in basic research, X3.

Specify the model form and then carefully and completely indicate how you would estimate the coefficients.

Do this first using an unrestricted model and then a second time including the restriction that the coefficients of the three variables should sum to 1.