Wednesday

August 20, 2014

August 20, 2014

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

- ECON -
**economyst**, Thursday, October 15, 2009 at 1:27pma) 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

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