Question

Suppose a firm has production function f(x1, x2) = x1 + x2. How much output should the firm produce in the long run?

Answer #1

There seems to be a perfect substitutability between the two inputs, X1 and X2. If assume that their prices are P1 and P2, then we have a long run equilibrium condition where MRTS = P1P2. In this case the marginal rate of technical substitution is 1 which indicates that the long run equilibrium condition has P2 = P1. Now if we observe that in the long run, P2>P1, it means using X2 is expensive and therefore the output is Q = X1.

Similarly, if we observe that in the long run, P2<P1, it means using X1 is expensive and therefore the output is Q = X2. This analysis indicates that the long run production depends upon the price level of two inputs.

Suppose the production function of a firm is given by f (x1; x2)
= min{x1, x2}
(a) Calculate the conditional demand functions of the firm
assuming w1 = 2; w2 = 4, and y = 8
(b) Calculate the minimum cost of the firm to produce 8 units of
the good when w1 = 2 and w2 = 4:

1. A ﬁrm has two variable factors of production, and its
production function is f(x1,x2) = x1/2 1 x1/4 2 . The price of the
output is 6. Factor 1 receives the wage $2, and factor 2 receives
the wage $2. a. How many units of each factor will the ﬁrm demand?
b. How much output will it produce?
2. Beth produces software. Her production function is f(x1,x2) =
3x1 + 2x2, where x1 is the amount of unskilled labor...

2 .Suppose the production function of a firm is given by f (x1,
x2) = 2x1 + 4x2
(a) Calculate the conditional demand functions of the firm
assuming w1 = 2; w2 = 3, and y = 8
(b) Calculate the minimum cost of the firm to produce 8 units of
the good when w1 = 2 and w2 = 3

A competitive firm’s production function is f(x1,x2)=
24x1^1/2x2^1/2. The price of factor 1 is 1, the price of factor 2
is 2 and the price of output is 4. (a) Write down the cost function
in terms of both the inputs. (b) What is the long-run cost
minimization condition for this firm? (c) In what proportions
should x1 and x2 be used if the firm wants to minimize its
costs?

1. Consider a firm with technology that can be represented by
the following production function: f(x1, x2) = min {x1, x2} +
x2
Input 1 costs w1 > 0 per unit and input 2 costs w2 > 0 per
unit.
(a) Draw the isoquant associated with an output of 4. Make sure
to label any intercepts and slopes.
(b) Find the firm’s long-run cost function, c(w1, w2, y)

Consider production function f (x1, x2) =
x11/2x21/3. The price
of factor 1 is w1 = 12
and the price of factor 2 is w2 = 1.
With x̄2 = 8, find the short-run cost function c(y).
Find short-run AC(y), AVC(y), and MC(y) based on the answer to
a.
Write out the long-run cost minimization problem to find the
cheapest way to produce y units of output.
Write out the Lagrangian for the long-run cost minimization
problem.
Solve the long-run...

Consider a firm with production function given by f(x1, x2) =
(x1)^1/4 (x2)^1/2 :
Assume the prices of inputs 1 and 2 are w1 and w2, respectively,
and the market price of the product is p.
(a) Find the levels of the inputs that maximize the profits of
the firm (X1, X2)
(b) Derive the supply function of the firm (i.e., y = f (x 1 ; x
2 ))

A firm’s production function is given as y=(x1)^(1/2) *
(x2-1)^(1/2) where y≥0 for the output, x1≥0 for the input 1 and
x2≥0 for the input 2. The prices of input 1 and input 2 are given
as w1>0 and w2>0,
respectively. Answer the following questions.
Which returns to scale does the production function
exhibit?
Derive the long-run conditional input demand functions and the
long-run cost function.

Suppose the market price that a firm can sell its product for is
a function of how much it and the firm's competitor produce so that
p = 136 - (x1 + x2) where p is the selling price, x1 is the firm's
production, and x2 is the competitor s production. The firm's cost
function is 28 + 3.6*x1. If the firm's competitor produces x2 = 27
units, how much should the firm produce if it wants to maximize the...

Suppose all firms in the market are identical with the following
production function.
x = f(l,k) = A l
bk b
Also, each firm faces a recurring fixed cost FC.
a. Now let A=30, b = 1/3, FC = 1,000,
w = 10 and r = 15. What is the long-run
equilibrium price of output? How many units of output does each
firm produce?
Suppose the market demand is 50,000,000/P2
b. How many firms are in the market in the...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 33 minutes ago

asked 36 minutes ago

asked 55 minutes ago

asked 58 minutes ago

asked 59 minutes ago

asked 59 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago