Question

PLEASE CHECK AND CORRECT MY ANSWERS!!!!

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

Answer 1

a) It should be (1/2)[x1^(-1/2)][x2^)3/2)

b) I think decreases. Plug in an example. If x1 grows x1^(-1/2) gets smaller.
c) the MP is correct. I think increases. Again, plug in an example. if x2 grows x2^(1/2) gets bigger.
d) I agree
e) i agree
f) I agree
g) I disagree. As the sum of the two exponents is > 1, this implies an increasing return to scale. Plug in an example. Increase x1 and x2 by some z percentage. Does output grow by more than z percent