Question

In: Economics

For the following two functions prove whether each of the production functions has increasing, decreasing, or...

For the following two functions prove whether each of the production functions has increasing, decreasing, or constant returns to scale. Then find whether the MPL is increasing, decreasing or constant with L.

A. ? = ?^1/3?^1/3

B. ? = 3?^3/2

Solutions

Expert Solution

Ans. To check whether the function has increasing, decreasing or constant returns to scale, we will increase the each input by proportion t and if after this, output increases by t then there is constant returns to scale, more than t then there is increasing returns to scale and less than t then there is decreasing returns to scale.

And MPL is increasing if it is positive, decreasing if it is negative and constant if MPL is equal to constant.

a) q = L^1/3 * K^1/3

For returns to scale,

q' = (tL)^1/3 * (tK)^1/3 = t^2/3 *K^1/3 * L^1/3 = t^2/3 *q < tq

So, decreasing returns to scale.

Marginal product of labour, MPL = dq/dL = 1/3*K^1/3 * L^(-2/3) > 0

Hence, MPL is increasing

b) q = 3L^3/2

For returns to scale,

q' = 3*(tL)^3/2 = t^3/2 * 3*L^3/2 = t^3/2 q > tq

So, increasing returns to scale.

Marginal product of labour, MPL = dq/dL = 9/2 * L^1/2 > 0

Hence, MPL is increasing.

* Please don’t forget to hit the thumbs up button, if you find the answer helpful.


Related Solutions

Do each of the following production functions exhibit decreasing, constant or increasing returns to scale? Prove...
Do each of the following production functions exhibit decreasing, constant or increasing returns to scale? Prove your answers. • Q = .5L.34 + K.34 • Q = [min (K, 2L)]2 • Q = (0.3L.5 + 0.7K.5)2 • Q = 4KLM where K, L, M are inputs
For each of the following production functions, determine whether it exhibits increasing, constant or decreasing returns...
For each of the following production functions, determine whether it exhibits increasing, constant or decreasing returns to scale: a) Q = K + L b) Q = L + L/K c) Q = Min(2K,2L) d) Q = (L5 )(K5)
Show whether each of the following production functions exhibit increasing, decreasing or constant returns to scale....
Show whether each of the following production functions exhibit increasing, decreasing or constant returns to scale. Q = 0.5KL                                                                                                             [2.5 Marks] Q = 2K + 3L                                                                                                           [2.5 Marks] A firm has the following production function                                   Q = 2(XY) 0.5 Where, X is maize and Y is rice. The cost of maize is K10 and the cost of rice Is K40. The firm has a budget of K80 to spend on the two goods. Formulate the firms’ optimization problem.                                                             [5...
Show whether the following production functions exhibit increasing, constant, or decreasing returns to scale. a. Q...
Show whether the following production functions exhibit increasing, constant, or decreasing returns to scale. a. Q = 2L + 3K b.   Q = L + 5K + 10 c.  Q = min (2*L, K) d.   Q = 10*K*L e.  Q = L2 + K2 f.   Q = K.5*L.5/2 + 10
1. For each of the following production functions, determine if the tech- nology exhibits increasing, decreasing,...
1. For each of the following production functions, determine if the tech- nology exhibits increasing, decreasing, or constant returns to scale. a. f(L; K) = L + K b. f(L; K) = p L + p K c. f(L:K) = LK + L + K d. f(L; K) = p KL + L + K 2. Draw isoquant maps for the following technologies. i) f(L; K) = LK ii) g(L; K) = L + 2K iii) h(L; K) = min(2L;...
Show whether the following production functions exhibit increasing, constant, or decreasing returns to scale in K and L.
Show whether the following production functions exhibit increasing, constant, or decreasing returns to scale in K and L. Note: “exponents add up to one, so it CRTS” is not an acceptable answer. a. Y=(K1-a + L1-a ) 1/a b. Y=K/L c. Y=K1/4L3/4
3. Do each of the following production functions exhibit decreasing, constant or increasing returns to scale?...
3. Do each of the following production functions exhibit decreasing, constant or increasing returns to scale? Prove your answers. • Q = .5L^.34 + K^.34 • Q = [min (K, 2L)]^2 • Q = (0.3L^.5 + 0.7K^.5)^2 • Q = 4KLM where K, L, M are inputs
. Under what conditions on a and b do the following production functions exhibit decreasing, increasing...
. Under what conditions on a and b do the following production functions exhibit decreasing, increasing or constant returns to scale? Mathematically justify and show your work. a. Q(L,K) = aL + bK b. Q(L,K) = (La + Ka ) 1/b
Do the following production functions have increasing, decreasing, or constant returns to scale? Which ones fail...
Do the following production functions have increasing, decreasing, or constant returns to scale? Which ones fail to satisfy the law of diminishing returns? ? = min(??, ??) ?=?10.3 ?20.3 ?0.3
identify whether the following scenario is an example of increasing or decreasing competition and intraspecific or...
identify whether the following scenario is an example of increasing or decreasing competition and intraspecific or interspecific competition. Zebra mussels being introduced to the Great Lakes __________,___________ Culling the wolf population in Northern Alberta to preserve the caribou population________________-,________________ Cichlids in Lake Victoria, evolving into more than 500 different species ________________,_________________ Bison population migrating from B.C. to Northern Alberta during mating season______________,____________
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT