Question

A price-taking firm has production function: ?? = ??????/??????/?? This is a long-run problem. Labor and capital cost w and r, respectively. Show that the long-run Total Cost function is ???? = ?? ?? ?? ???? ??/?? ??

Answer #1

A price-taking firm has production function: q41/4K1/4 This is a
long-run problem. Labor and capital cost w and r, respectively.
Show that the long-run Total Cost function is TC-2 (rw Hint:This is
just like the consumption problem where you derive the Hicks demand
functions then the expenditure function

a firm produces a product with labor and capital as inputs. The
production function is described by Q=LK. the marginal products
associated with this production function are MPL=K and MPK=L. let
w=1 and r=1 be the prices of labor and capital, respectively
a) find the equation for the firms long-run total cost curve
curve as a function of quantity Q
b) solve the firms short-run cost-minimization problem when
capital is fixed at a quantity of 5 units (ie.,K=5). derive the...

A firm produces a product with labor and capital. Its production
function is described by Q = min(L, K). Let w and r be the prices
of labor and capital, respectively.
a) Find the equation for the firm’s long-run total cost curve as
a function of quantity Q and input prices, w and r.
b) Find the solution to the firm’s short-run cost minimization
problem when capital is fixed at a quantity of 5 units (i.e., K =
5). Derive...

A firm’s production function is Q! = min(4L ,5K ). The price of
labor is w and the price of capital is r.
a) Derive the demand function of labor and capital respectively.
How does the demand of capital change with the price of
capital?
b) Derive the long-run total cost function. Write down the
equation of the long-run expansion path.
c) Suppose capital is fixed at K = 8 in the short run. Derive
the short-run total cost function....

A hat manufacturing ﬁrm has the following production function
with capital and labor being the inputs: Q = min(5L,3K) (it has a
ﬁxed-proportions production function). If w is the cost of a unit
of labor and r is the cost of a unit of capital, derive the ﬁrm’s
optimal inputs, long-run total cost curve, average cost curve, and
marginal cost curve in terms of the input prices and Q.
b) A ﬁrm has the linear production function Q = 2L...

Suppose a firm has a production function given by q = 3L +
K.
The firm can purchase labor, L at a price w = 24, and capital, K
at a price of r = 5.
What is the firm’s total cost function?

A firm produces output according to the production function.
Q=sqrt(L*K) The
associated marginal products are MPL = .5*sqrt(K/L) and MPK =
.5*sqrt(L/K)
(a) Does this production function have increasing, decreasing, or
constant marginal
returns to labor?
(b) Does this production function have increasing, decreasing or
constant returns to
scale?
(c) Find the firm's short-run total cost function when K=16. The
price of labor is w and
the price of capital is r.
(d) Find the firm's long-run total cost function...

2. A firm has production function Q = k^1/2L^1/2 and faces a
wage for the labor input w = 1 and a rental price of capital r =
9
a. The policy of the Federal Reserve brings the rental price of
capital to r = 4 Graph the change of the cost minimizing equlibrium
explaining the type of substitution that is happening.
b. Compute the new cost function. Suppose a monopoly and show
graphically if after this change in the...

A firm’s production function is Q(L,K) = K^1/2 + L. The firm
faces a price of labor, w, and a price of capital services, r.
a. Derive the long-run input demand functions for L and K,
assuming an interior solution. If the firm must produce 100 units
of output, what must be true of the relative price of labor in
terms of capital (i.e. w/r) in order for the firm to use a positive
amount of labor? Graphically depict this...

Given the production function Q=K2L2 and
the price of capital and labor as r=4 and w=8, respectively, if the
goal is Q=2500 find the level of capital (K) and labor (L) to
minimize cost.

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