Question

1. An economy has a total of 320 units of labor and 80 units of capital to use on
the production of 2 goods. The production functions for the goods are a function
of the labor and capital used in each process. Specifically,

x=F(l_x, K_x)= (l_x* K_x)^1/2
y = G(l_y, K_y)^1/2l

a) Find the production of each good if x is given 40 labor and 40 capital y has the
rest of the resources. Find the specific value of the RTS for each production
process with the current distribution of resources. Use this information to help you
re-allocate the resources in a way that leads to more of both goods being
produced. Explains why this proves the first (x,y) in this problem is not a point on
the PPF for this economy. there are many correct ways to redistribute the
resources.)

c) Explain why at any point on the PPF, each firm always has 4 times more labor
than capital.

d. If (c) is correct, then both the quantity of x and y can be written solely as a
function of K_x. Find these functions, then use them to prove that the PPF function
for this economy is y = 800 – 5x.

Answer 1