In any given time period t, the representative rm uses the Cobb'Douglas produc+ tion technology: Ar-f(knntl :At-kfinrl_me in producing its output of goods and services. As standard, the exponent a; E (U, l) in every period t, but note here that the exponent could be different in dif- ferent time periods. The rest of the notation is identical to that used in Chapter 6. In the early 20th century, U.S. rms used less capital in their production process than they did in the early let century. For simplicity, suppose that total factor productivity did not change at all during the century. And further suppose that neither real wages nor real interest rates changed at all during the century. If the representative rm (which, as per usual economic analysis, maximizes its economic prots) uses a larger ratio of capital to labor (that is, a larger prot- maximizing ratio :51) in the early 21st century compared to the early 20th century, what change(s) must have occurred? Base the analysis on the given production function. Provide brief yet complete mathematical justication and a brief economic interpretation