11.6 Show that for the constant returns-to-scale CES production function q = [Kf + LPY^

a. MPK = (^\~P and MPL = (j-\~"

b. RTS=[ — ) . Use this to show that cr = 1/(1 - p).

\K I

c. Determine the output elasticities for Xand L. Show that their sum equals 1.

d. Prove that Hence, show Note: The latter equality is useful in empirical work, because in some cases we may approximate dq/dL by the competitively determined wage rate. Hence, a can be estimated from a regression of ln(q/L) on in w.