6.5 Conclusion

On the one hand, what we did in this lecture was pretty simple: we took one formula \(\left.{dy \over dx}\right|_{f(x,y) = z} = - {\partial f/\partial x \over \partial f/\partial y}\) and applied it to two examples: the formula for the slope of an isoquant is \(MRTS = {\partial f(L,K)/\partial L \over \partial f(L,K)/\partial K} = {MP_L \over MP_K}\) and the formula for the slope of the PPF is \(MRT = {\partial L(x_1,x_2)/\partial x_1 \over \partial L(x_1,x_2)/\partial x_2 } = {1/MP_{L1} \over 1/MP_{L2} }\) In each of these cases, we used some economic logic to analyze what exactly was going on as one moved along each of these curves:

• An isoquant represents a tradeoff between labor and capital. The relative productivities of labor and capital determine the rate of this tradeoff.
• A PPF represents a tradeoff between two goods. The relative productivities of resources in producing these goods determine the rate of this tradeoff.

This is challenging stuff, and the homework is hard. Be sure you balance your ability to do the (necessary!) procedural aspects of the homework with some building of intuition as to what those procedures are actually doing.