11.10 Some envelope results Young’s theorem can be used in combination with the envelope results in this chapter to derive some useful results.

a. Show that @l(P, v, w)/@v ¼ @k(P, v, w)/@w. Interpret this result using substitution and output effects.

b. Use the result from part

(a) to show how a unit tax on labor would be expected to affect capital input.

c. Show that @q/@w ¼ %@l/@P. Interpret this result.

d. Use the result from part

(c) to discuss how a unit tax on labor input would affect quantity supplied.