Question

For each of the following production functions, (i) sketch an isoquant, (ii) indicate whether each marginal product is diminishing, constant, or increasing points, and (iii) indicate whether the production function shows constant, decreasing, or increasing returns to scale.

A) Q = f(L, K) = L^{2}K^{3}

B) Q = f(L, K) = 2L + 6K

C) Q = f(L, K) = (*min*L, K) ^{(1/2)}

Answer #1

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 = (L.5
)(K.5)

1. Given the following production functions determine whether
the production functions exhibit increasing, decreasing, or
constant returns to scale for all levels of output.
a) Q = L0.3K0.2
b) Q = (L+0.01K)0.8
c) Q = min[2L,K]

Determine whether the following production functions exhibit
increasing, decreasing or constant returns to scale.
a. Q = L + K
b. Q = 10KL
c. Q = L + K1/2L 1/2 + K
d. Q = 10K1/4L 1/4

2. Consider the following production functions, to be used in
this week’s assignment:
(A) F(L, K) = 20L^2 + 20K^2
(B) F(L, K) = [L^1/2 + K^1/2]^2
a (i) Neatly draw the Q = 2,000 isoquant for a firm with
production function (A) given above, putting L on the horizontal
axis and K on the vertical axis. As part of your answer, calculate
three input bundles on this isoquant. (ii) Neatly draw the Q = 10
isoquant for a firm...

Determine which of the following production functions exhibit
decreasing returns to scale,
increasing returns to scale, or constant returns to scale.
Q = K/(L)^2
Q = 4K + 2L
Q = a KL

1. Show whether the following production functions exhibit
decreasing returns to scale (DRS), constant returns to scale (CRS),
or increasing returns to scale (IRS)?
a. q = 10L^0.6 K^0.5
b. q = L + K
c. q = L^0.6 + K^0.5

5. Decide whether the following production functions belong to
increasing, constant, or decreasing returns to scale?
Q = L^0.3·K60.5
Q = L·K^0.5
Q = L·lnK
Q = L+K^0.8
Q = L+395K

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?

For each of the following production
functions,
• Write an equation and graph the isoquant for Q =
100.
• Find the marginal rate of technical substitution and
discuss how MRTSLK changes as the ?rm uses more L, holding output
constant.
(c) Q(K,L) = LK + L

Suppose that you are given the
following production function:
Q =
100K0.6L0.4
For each of the following
production functions, determine whether returns to scale
are decreasing, constant, or increasing when capital and labor
inputs are increased from K = L =
1 to K = L = 2.
a. Q =
25K0.5L0.5
b. Q =
2K + 3L + 4KL

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