Question

. 1

a) Calculate the corresponding cost function, c(w,r,q).

·q=(min(L,3K))^{.5}

·q=L-1/K

b) Draw a representative isoquant for q=12

·Q=min(2L,(2(L+K))/3,2K)

Answer #1

A firm’s production function is Q = min(K , 2L), where Q
is the number of units of output produced using K units of capital
and L units of labor. The factor prices are w = 4 (for labor) and r
= 1 (for capital). On an optimal choice diagram with L on the
horizontal axis and K on the vertical axis, draw the isoquant for Q
= 12, indicate the optimal choices of K and L on that isoquant,...

3. A firm’s production function is Q=min(K, 3L ). Input prices a
re as follows: w=$ 2 and r=$1.
On the optimal choice diagram below, draw the isoquant for Q=12.
Calculate the optimal choice of K and L for this level of output as
well as the total cost.
Then, draw in (with a dotted line) the isocost line consistent
with your Total Cost value.
It won't let me copy the graph template but it is a simple graph
with...

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.

For a firm with production function f(L,K)=√L+√K, find its cost
function for arbitrary values of w and r. That is,find a formula
for the cost of producing q units that includes q,and also w and
r,as variables. Also find marginal and average cost,and draw a plot
that shows both cost functions in the same graph.

For a firm with production function f(L,K)=√L+√K, find its cost
function for arbitrary values of w and r. That is,find a formula
for the cost of producing q units that includes q,and also w and
r,as variables. Also find marginal and average cost,and draw a plot
that shows both cost functions in the same graph.

The firms production function is: Q=2L^2/3 K^1/3
A) Suppose the firm wants to determine the cost minimizing
combination for L and K for any given values of q, w, and r. Solve
for the the firms factor demand functions for L and K (i.e. express
the optimal quantity of L and K in terms of W, r and Q)
B) Using these factor demand functions, solve for the firm's
long run cost function.

4. Suppose a small oil drill has the following production
function F(K,L) =
min(4K,L)
where every drill (captial unit) takes 4 people to operate.
Output is measured in barrels.
(a) Suppose there are 10 drills in the oil field. How many
workers are needed to produce 40 barrels of oil (q=40)?
(b) Graph the isoquant curves that represent q=20, q=40, and
q=60.
(c) Setup the cost minimization problem where labor and capital are
flexible. Then find the cost function if...

q(L,K)=2LK=100; w=25; v=50; TC=500
i. find the cost-minimizing input combinations (L*,K*)
ii Based on part i grapg this cost minimization case
iii. Now assume that w=30 and v=50. explain what happens to our
isocost and (L*,K*)
iv. Assume that w=25; v=50 repeat parts i and ii
a. q(L,K)=2L+K=100
b. q(L,K)=min(2L,K)=100

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...

1. Consider the production
function q=K2L0.5
a) Find the cost minimizing quantities of K and L for q = 100, r
as the price of K and w as the price of L.
b) Find the cost minimizing quantities of K and L for q = 1000,
r as the price of K and w as the price of L. Explain whether or not
the output expansion [change from part a) to part b)] is labor
saving or capital saving.

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