7. Use production function and MPK diagrams to examine Turkey and the
European Union (EU). Assume that Turkey and the EU have different
production functions $q = f(k)$, where $q$ is output per worker and $k$ is
capital per worker. Let $q=Ak^{13}$. Assume that the productivity level A in
Turkey is lower than that in the EU.
a. Draw a production function diagram (with output per worker y as a function of capital per
worker $k$) and MPK diagram (MPK versus $k$) for the EU. (Hint: Be sure to draw the two
diagrams with the production function directly above the MPK diagram so that the level of
capital per worker $k$ is consistent on your two diagrams.)
b. For now, assume capital cannot flow freely in and out of Turkey. On the same diagrams,
plot Turkish production function and MPK curves, assuming that the productivity level A
in Turkey is half the EU level and that Turkish MPK exceeds EU MPK. Label the EU
position in each chart EU and the Turkish position T1.
c. Assume capital can now flow freely between Turkey and the EU and the rest of the world,
and that the EU is already at the point where $MPK = r^*$. Label $r^*$ on the vertical axis of the
MPK diagram. Assume no risk premium. What will Turkey's capital per worker level $k$ be?
Label this outcome point T2 in each diagram. Will Turkey converge to the EU level of $q$?
Explain.
