Consider the production function Q = K + L. For this production function, MPL = 1/(2L) and

Question:

Consider the production function Q = K + √L. For this production function, MPL = 1/(2√L) and MPK = 1. Derive the input demand curves for L and K, as a function of the input prices w (price of labor services) and r (price of capital services). Show that at an interior optimum (with K > 0 and L > 0) the amount of L demanded does not depend on Q. What does this imply about the expansion path?