210 CHAPTER | 7 Case Study: Cost Models to Illustrate KLEM Data Rearranging, we have K = ð K K=PQÞ L = ð L L=PQÞ: (7.9) (7.10) One important implication of the log­log specification is that parameters K and L must equal value shares of inputs in the value of output. In their study on U.S. manufacturing over the 1899­1922 time period, Cobb and Douglas (1928) argued that if markets were competitive, if firms chose inputs so that marginal products equaled real prices, and if production technology in U.S. manufactur- ing over this timeframe followed the constant returns to scale log­log specifica- tion described earlier, then the ordinary least-squares (OLS) estimators of K and L should be approximately equal to 0.25 and 0.75, respectively. In fact, these estimates were consistent with actual shares of total product published by the National Bureau of Economic Research, which were 0.259 and 0.741 for K and L, respectively. ELASTICITIES OF SUBSTITUTION FOR COBB­DOUGLAS You may also recall from Chapter 5 the discussion that the substitution elasti-