suppose the production function is given by the equation q =
L(100K)^(1/2). graph the isoquants corresponding...
suppose the production function is given by the equation q =
L(100K)^(1/2). graph the isoquants corresponding to q = 200, q =
400, and q = 500 (give 3 points on the isoquant graph). do these
isoquants exhibit diminishing marginal rate of technical
substitution? prove your answer and show all work
Bonus Question. Suppose the production function for a firrm is
Q(K,L) = K1/2L1/2, so the marginal...
Bonus Question. Suppose the production function for a firrm is
Q(K,L) = K1/2L1/2, so the marginal product of labor is MPL = 1 2
K1/2L−1/2 and the marginal product of capital is MPK = 1 2
K−1/2L1/2.
a) Find the equation of the isoquant for Q = 1. That is, when Q
= 1, find L as a function of K or K as a function of L to obtain an
equation for the isoquant.
b) Find K1, K2, L3,...
For each of the following production
functions,
• Write an equation and graph the isoquant for...
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
1. (a) Based on the production function: Q = 2K1/2L1/2, please
draw the isoquant with Q=10....
1. (a) Based on the production function: Q = 2K1/2L1/2, please
draw the isoquant with Q=10.
(b) Given r=1; w=2, please draw the isocost with TC=27, on the
same graph.
(c) Based on the isoquant and isocost curves you drew, is TC=27
the cheapest cost of producing Q=10? Is Q=10 the maximum quantity
given TC=27? Explain.
Suppose a firm’s production function is given by Q = L 1/2 , K
1/2.
a)...
Suppose a firm’s production function is given by Q = L 1/2 , K
1/2.
a) Suppose the firm has a fixed cost FC=6, the price
of labor is w = 64 and the price of capital is r = 4. Derive the
firm’s total cost function, TC(Q).
b) What is the firm’s marginal cost?
c) Graph the firm’s isoquant for Q = 20 units of
output. On the same graph, sketch the firm’s isocost line
associated with the total...
Draw isoquant curve for the following production functions.
Here ?Kdenotes quantity of capital input and ?Ldenotes...
Draw isoquant curve for the following production functions.
Here ?Kdenotes quantity of capital input and ?Ldenotes the
quantity of labor input.
In the graph, let ?Kbe on the vertical axis and ?Lbe on the
horizontal axis.
(a) ?(?,?)=?⋅?=?¯,F(K,L)=K⋅L=Q¯,where
(1) ?¯=100,Q¯=100,
(2) ?¯=200,Q¯=200,
(3) ?¯=300.Q¯=300.
This production function is an example of Cobb-Douglas
production technology.
(b) ?(?,?)=2?+5?=?¯,F(K,L)=2K+5L=Q¯,where
(1) ?¯=100,Q¯=100,
(2) ?¯=200,Q¯=200,
(3) ?¯=300.Q¯=300.
This production function is an example of perfect substitutes
production technology.
(c) ?(?,?)=min{2?,5?}=?¯,F(K,L)=min{2K,5L}=Q¯,where
(1) ?¯=100,Q¯=100,
(2) ?¯=200,Q¯=200,
(3)...
Draw isoquant curve for the following production functions.
Here ?Kdenotes quantity of capital input and ?Ldenotes...
Draw isoquant curve for the following production functions.
Here ?Kdenotes quantity of capital input and ?Ldenotes the
quantity of labor input.
In the graph, let ?Kbe on the vertical axis and ?Lbe on the
horizontal axis.
(a) ?(?,?)=?⋅?=?¯,F(K,L)=K⋅L=Q¯,where
(1) ?¯=100,Q¯=100,
(2) ?¯=200,Q¯=200,
(3) ?¯=300.Q¯=300.
This production function is an example of Cobb-Douglas
production technology.
(b) ?(?,?)=2?+5?=?¯,F(K,L)=2K+5L=Q¯,where
(1) ?¯=100,Q¯=100,
(2) ?¯=200,Q¯=200,
(3) ?¯=300.Q¯=300.
This production function is an example of perfect substitutes
production technology.
(c) ?(?,?)=min{2?,5?}=?¯,F(K,L)=min{2K,5L}=Q¯,where
(1) ?¯=100,Q¯=100,
(2) ?¯=200,Q¯=200,
(3)...
6.7 The production function
Q=KaLb where 0≤ a, b≤1 is called a Cobb-Douglas production
function. This...
6.7 The production function
Q=KaLb where 0≤ a, b≤1 is called a Cobb-Douglas production
function. This function is widely used in economic research. Using
the function, show the following:
a. The production function in Equation 6.7 is a special case of
the Cobb-Douglas.
b. If a+b=1, a doubling of K and L will double q.
c. If a +b < 1, a doubling of K and L will less than double
q.
d. If a +b > 1, a doubling...