Substitution and Expansion Effects in Production: The General Case of Joint Production

This chapter aims to extend the axiomatic approach to input demand theory with a single output, which was taken in Chap. 6 , to the more general case of joint production. Although such an extension from one output to several outputs seems to be straightforward, it nevertheless requires special care and careful interpretations. More specifically, it is concerned with a systematic examination of what happens when a firm that has been in equilibrium at certain prices of inputs and prices of outputs experiences a change in one of these prices. The mutual effects between inputs between inputs (or between outputs), the cross effects between inputs and outputs are newly explored by means of various kinds of decomposition equations in production theory. Those decomposition equations teach us that the total effect of an input price (or an output price) can be decomposed into the two separate effects; namely, the substitution effect along on the old isoquant frontier (or the old transformation frontier) and the expansion effect along the new expansion path associated with input prices (or output prices). Finally, a new definition of the normal technology is given to show that inputs are not gross substitutes, nor are outputs, and that the input–output relations are not regressive.