Question
In: Economics
If x1 and x2 are the factors of production of a typical firm, output price is...
If x1 and x2 are the factors of production of a typical firm, output price is p, price of x1 and x2 are w1 and w2, respectively and the firm’s production function is:
f (x1, x2) = x1^3 x2^3
i. Write up firm’s short run and long run profit maximization problem. Show firm’s short run profit maximization graphically please.
ii. Using the information above can you write the cost minimization problem for this firm if the firm decides to produce y1 level of output? Please show graphically how the firm minimizes its costs. What is the alternative method we can use to find the optimal quantity of x1 and x2 to solve the cost minimization problem for the firm? Explain.
iii. If the firm’s factor demand functions for x1 and x2 are as follows:
x1= p ^3/ (27 w1^2 w2)
x2= p ^3/ (27 w1 w2^2)
a. How the optimal quantity of each input changes when price of input changes?
b. How the optimal quantity of one input changes when price of other input changes?
c. How the optimal quantity of each input changes when price of that input changes?
Solutions
Rahul Sunny answered 2 years agoRelated Solutions
The production function of a competitive firm is given by f(x1, x2) = x1^1/3 (x2 −...
The production function of a competitive firm is given by f(x1,
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Compute the firm’s cost function c(y). (b) Compute the marginal and
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Suppose that a firm has the p production function
f(x1; x2) = sqrt(x1) + x2^2.
(a) The marginal product of factor 1 (increases,
decreases, stays constant) ------------ as the amount of factor 1
increases. The marginal product of factor 2 (increases, decreases,
stays constant) ----------- as the amount of factor 2
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(b) This production function does not satisfy the
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A firm has two variable factors and a production function
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u(x1, x2) = min {x1/2, x2/3} if the price of good 1 is $7/unit, the price...
u(x1, x2) = min {x1/2, x2/3}
if the price of good 1 is $7/unit, the price of good 2 is
$4/unit and income is 114..
What is this person's optimal consumption level for good 2?
Suppose there are 2 goods, x1 and x2. The price of x1 goes up. x1 is...
Suppose there are 2 goods, x1 and x2. The price of x1
goes up. x1 is inferior, and x2 is normal. Using income and
substitution effects, show which of the claims below is
correct.
Question options:
x1 will decrease in quantity, but x2 will go up
x1 may increase or decrease in quantity, the same is true for
x2
the quantity of both goods will go down
the quantity of both goods will go up
Over an initial range of output marginal cost of widget production by the typical firm is...
Over an initial range of output marginal cost of widget
production by the typical firm is constant; above that range it
rises. The cost function of a typical firm is given by:
TCi = 390 +
10qi
for qi £ 50
= 390 + 10qi + 0.1(qi -
50)2 for
qii> 50
Demand for widgets is given by: q = 1440 - 50p
(e) If market demand falls drastically to q = 700 - 50p, what
will be...
Consider a firm using the following long-run technology: q=f(x1,x2)=1/3ln(x1)+1/6ln(x2) Where output and input prices are given...
Consider a firm using the following long-run technology:
q=f(x1,x2)=1/3ln(x1)+1/6ln(x2) Where output and input prices are
given by the non-negative constant vector (p,w1=2,w2=1). Which of
the following is the correct expression for the firm's optimized
profit function π(p)?
1/2(ln(p/6)−1)
1/2p(ln(p/6)−1)
1/2p(ln(p/6)+1)
1/2(ln(p/6)+1)
. Consider a firm that has a production function y = f(x1, x2) = 2x 1/4...
. Consider a firm that has a production function y = f(x1, x2) =
2x 1/4 1 x 1/4 2 facing input prices w1 = 2
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• What will be the profit maximizing output level?
-What will be the profit? •
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Consider a perfectly competitive firm that produces output using a wellbehaved production function y = f(x1,x2)....
Consider a perfectly competitive firm that produces output using
a wellbehaved production function y = f(x1,x2). Let the price of
output be denoted by p, the price of input 1 be denoted by w1, and
the price of input 2 be denoted by w2.
(a) State the firm’s cost-minimization problem, and draw the
solution to the cost minimization problem on a graph.
(b) What are the solutions to the cost-minimization problem? What
are these solutions called? Which variables are these...
Consider a perfectly competitive firm that produces output using a wellbehaved production function y = f(x1,x2)....
Consider a perfectly competitive firm that produces output using
a wellbehaved production function y = f(x1,x2). Let the price of
output be denoted by p, the price of input 1 be denoted by w1, and
the price of input 2 be denoted by w2.
j) Suppose x2 is fixed at some level x2. Graph the
solution to the profit maximization problem where profit is maximized
by choosing x1. [Note that this profit maximization problem is the
short-run version of the profit...
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