10.7 How would you expect an increase in output price, P, to affect the demand for capital and labour inputs?

a.

Explain graphically why, if neither input is inferior, it seems clear that a rise in P must not reduce the demand for either factor.

b.

c.

Show that the graphical presumption from part (a)

is demonstrated by the input demand functions that can be derived in the Cobb–Douglas case.

Use the proit function to show how the presence of inferior inputs would lead to ambiguity in the effect of P on input demand.

−a�k*

�Pb

�q*

�P = �q s

�P +

.

�k*

�v Do this in three steps. First, differentiate the definitional relation with respect to P using the chain rule. Next, differentiate the definitional relation with respect to v (again using the chain rule) and use the result to substitute for ∂qs/∂k in the initial derivative. Finally, substitute a result analogous to part

(c) of Problem 10.8 to give the displayed equation.

b.