Question

3. Yasmin (Y) and Xavier (X) run firms that produce goods using capital (K) and labor (L). They each have technologies such that the Marginal Product of Capital is given by L (the amount of labor hired by the firm) and the Marginal Product of Labor is given by K (the amount of capital used by the firm). Thus, for Yasmin, the marginal rate of technical substitution for her firm is given by where the subscript indicates that this is the amount of the input used by Yasmine's firm. Similarly, the marginal rate of technical substitution for Xavier's firm is given by X. Suppose that there are 100 workers and 100 units of capital available and that Yasmin and Xavier runs the only firms that produce goods in this economy. What allocations of capital and labor will satisfy Production Efficiency? Show your work.

Answer 1

for productive efficiency, the MRTS of both lamina should be equal re Kx = kx (only then the a wrices will be). LX Ly tangent to cech other since there are only 100 units of labor and capital therefore I Kx + Ky=100 and Lx+Ly=100 Hence any allocetion such that kx = 100 - kby will be an LX 100- Ly efficient production Escample (Kx, Lx ) =(40,40), (ky, Ly ) = (60.00