April 16, 2014

Homework Help: ECON

Posted by Anonymous on Wednesday, October 14, 2009 at 8:41pm.


MRTS = marginal rate of technical substitution
RTS = returns to scale
MP = marginal product

Suppose the production function is Cobb-Douglas and f(x1, x2) = [x1^(1/2)][x2^(3/2)]. (Note: x1 and x2 are variables).

a) Select an expression for MP of factor 1 at point (x1, x2).
b) MP of factor 1 ___ for small increases in x1, holding x2 fixed.
c) MP of factor 2 is _____ and it ____ for small increases in x2.
d) An increase in the amount of x2 _____ the MP of factor 1.
e) The technical rate of substitution between x2 and x1 is _____.
f) Does this technology have a diminishing technical rate of substitution?
g) This technology demonstrates ____ returns to scale.

My answers:
a) [x1^(-1/2)][x2^(3/2)]
b) increases
c) [3/2][x1^(1/2)][x2^(1/2)], decreases
d) increases
e) -(x2)/(3x1)
f) yes
g) decreasing

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