Question

The production function for the Roundtree Laser Company is: Q=(10L^.5)(K^.3)(M^.3)

where: Q: number of lasers produced per week L: amount of labor used per week K: the amount of capital used per week M: quantity of raw materials used per week

a) Does the production function exhibit decreasing returns to scale?

b) Does the production function exhibit diminishing marginal returns?

Answer #1

(a) No, for this cobb-douglas production function to exhibit decreasing returns to scale, the sum of the power coefficients of L,K and M should be less than 1. But here it is 0.5+0.3+0.3=1.1 which is greater than 1. This production function exhibits increasing returns to scale.

(b) Yes this production Function exhibits diminishing marginal returns. To check this we double differentiate the production function w.r.t to L,K and M.

Since all are negative, so we have diminishing marginal returns.

2. Bridgestone Company has
the following production function for tires: Q = 20 K
0.2 L 0.8, where K represents machine hours
and L represents labor hours. They pay $ 15 per hour to rent their
machines and $ 10 per hour to their workers. They have $ 12,000 to
spend on capital and labor.
A. Does this production function
exhibit constant, increasing, or decreasing returns to scale?
B. Does this production function
exhibit diminishing marginal returns to capital and...

Wheat is produced according to the production function Q = 100
K^0.8 L^0.2
a. Beginning with a capital input of 4 and a labor input of 49,
show that the marginal product of labor and the marginal product of
capital are both decreasing.
b. Does this production function exhibit increasing, decreasing,
or constant returns to scale?
please explain in 4 sentences thank you!

The production function for a firm is Q = −0.6L 3 + 18L 2K + 10L
where Q is the amount of output, L is the number of labor hours per
week, and K is the amount of capital.
(a)Use Excel to calculate the total short run output Q(L) for L
= 0, 1, 2...20, given that capital is fixed in the short run at K =
1.
(b) Use Excel to calculate the total long run output Q(L) for...

2. A firm has the following linear production function:
q = 5L + 2K
a. Does this firm’s production function exhibit diminishing
returns to labor?
b. Does this production function exhibit diminishing returns to
capital?
c. Graph the isoquant associated with q = 20.
d. What is the firm’s MRTS between K and L?
e. Does this production technology exhibit decreasing, constant,
or increasing returns to scale?

Consider the production function Q = f(L,K) = 10KL / K+L. The
marginal products of labor and capital for this function are given
by
MPL = 10K^2 / (K +L)^2, MPK = 10L^2 / (K +L)^2.
(a) In the short run, assume that capital is fixed at K = 4.
What is the production function for the firm (quantity as a
function of labor only)? What are the average and marginal products
of labor? Draw APL and MPL on one...

Consider the following production function q
= K2 + L2.
Does this production function exhibit constant, increasing or
decreasing returns to scale?)
Find an expression for the marginal rate of technical
substitution. Does this production function exhibit diminishing
marginal rate of technical substitution? Explain

Joe’s coffee house operates under the production function Q =2√?
+ ?^2/3, where L is the number of worker hours and K is the number
of coffee machine hours.
a. Clearly show what type of returns to scale is exhibited.
b. Does labor exhibit diminishing marginal returns when capital
is fixed? Explain.

An electronics plant’s production function is Q = L 2K, where Q
is its output rate, L is the amount of labour it uses per period,
and K is the amount of capital it uses per period.
(a) Calculate the marginal product of labour (MPL) and the
marginal product of capital (MPK) for this production function.
Hint: MPK = dQ/dK. When taking the derivative with respect to K,
treat L as constant. For example when Q = L 3K2 ,...

Production function, Q = 10L +
5K0.9+10L0.5K0.4 is subject
to:
a) increasing returns to scale.
b) decreasing returns to scale.
c) constant returns to scale.
d) economies of scope.
e) diseconomies of scope.

a firm produces its output (y) using three inputs: capital (K),
labour (L) and materials (M). Its production function is y =
K0.2L0.5M0.3.
For which input(s) does production exhibit a diminishing
marginal product?
Select one or more:
a. capital
b. labour
c. materials
The firm’s production is characterised by
Select one:
a. decreasing returns to scale.
b. constant returns to scale.
c. increasing returns to scale.

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