Question

Now consider a quadratic polynomial production function ? = ?x^?. Assuming the input, x, is essential...

Now consider a quadratic polynomial production function ? = ?x^?. Assuming the input, x, is essential for production of y, what must be true of the signs and magnitudes of the parameter, ?, so that the production function is “well-behaved”? Provide mathematical proofs and word explanations in your answer.

Business   Economics   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

WELL BEHAVED PRODUCTION FUNCTION MEANS-

WHEN INPUTS ARE INCREASED WITH THE SAME PROPORTION SAY n THE OUTPUT ALSO INCREASES BY THE SAME PROPORTION n

THE PRODUCTION FUNCTION IS HOMOGENEOUS OF DEGREE 1

THIS IS ALSO CALLED LINEAR HOMOGENEOUS PRODUCTION FUNCTION

HENCE HERE WE NEED TO PROVE

F(nX) = nF(X)= nY

HENCE THE SIGN OF A IS POSITIVE AND MAGNITUDE IS 1

HOPE IT WAS HELPFUL FOR YOU. PLEASE GIVE IT A LIKE. THANKYOU!

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Question 1a Consider the polynomial function P(x) = x3+x2−20x. Sketch a graph of y = P(x)...
Question 1a Consider the polynomial function P(x) = x3+x2−20x. Sketch a graph of y = P(x) by: determining the zeros of P(x), identifying the y-intercept of y = P(x), using test points to examine the sign of P(x) to either side of each zero and deducing the end behaviour of the polynomial. b Consider the quadratic function f(x) = 2x2 + 8x−1. (a) Express f(x) in standard form. (b) Determine the vertex of f(x). (c) Determine the x- and y-intercepts...
Consider the quadratic function f, given by f(x) = −x2 + 6x−8. (i) Determine if the...
Consider the quadratic function f, given by f(x) = −x2 + 6x−8. (i) Determine if the graph of y = −x2 + 6x − 8 is concave up or concave down, providing a justification with your answer. (ii) Re-write the equation of the quadratic function f, given by f(x) = −x2 +6x−8, in the standard form f(x) = a(x−h)2+k by completing the square. Hence determine the vertex of the graph of y = f(x). (iii) Identify the x-intercepts and y-intercept...
Consider the Leontiev (perfect complements) production function f(x, y) = M in x 9.6 , y...
Consider the Leontiev (perfect complements) production function f(x, y) = M in x 9.6 , y 5.2 . (A) How many units of good y would be a perfect complement for 1 unit of good x? What is the equation of the firm’s kink line? (B) Assume the firm has a production quota of q = 400 units. Graph the firm’s level-400 isoquant. What are the coordinates of the kink? (C) Suppose the input prices are (px, py) = (16,...
Problem 3. Consider the Leontiev (perfect complements) production function f(x, y) = M in x 9.6...
Problem 3. Consider the Leontiev (perfect complements) production function f(x, y) = M in x 9.6 , y 5.2 . (A) How many units of good y would be a perfect complement for 1 unit of good x? What is the equation of the firm’s kink line? (B) Assume the firm has a production quota of q = 400 units. Graph the firm’s level-400 isoquant. What are the coordinates of the kink? (C) Suppose the input prices are (px, py)...
Consider the following production function: x = f(l,k) = Albkbwhere x is the output, l is...
Consider the following production function: x = f(l,k) = Albkbwhere x is the output, l is the labour input, k is the capital input, and A, b are positive constants. (a) Set up the cost minimization problem and solve for the first order conditions using the Lagrange Method. Let w be the wage rate and r the rental rate of capital. (b) Using your answer in (a), find how much labour and capital would the firm use to produce x...
Consider countries A and B with the same (unchanging) population. In country A, people devote 60%...
Consider countries A and B with the same (unchanging) population. In country A, people devote 60% of GDP to investment and the production function is Y=3√K, where Y denotes real GDP and K denotes the stock of physical capital. In country B, people devote 15% of GDP to investment and the production function is Y=5√K. a. Discuss the underlying intuition of the differences between countries A and B as described above (hint: there are two differences). b. Assume that both...
To illustrate the Mean Value Theorem with a specific function, let's consider f(x) = x^3 −...
To illustrate the Mean Value Theorem with a specific function, let's consider f(x) = x^3 − x, a = 0, b = 5. Since f is a polynomial, it is continuous and differentiable for all x, so it is certainly continuous on [0, 5] and differentiable on (0, 5). Therefore, by the Mean Value Theorem, there is a number c in (0, 5) such that f(5) − f(0) = f '(c)(5 − 0). Now f(5) = ______ , f(0) =...
Problem 1. Consider the Cobb-Douglas production function f(x, y) = 12x 0.4y 0.8 . (A) Find...
Problem 1. Consider the Cobb-Douglas production function f(x, y) = 12x 0.4y 0.8 . (A) Find the intensities (λ and 1 − λ) of the two factors of production. Does this firm have decreasing, increasing, or constant returns to scale? What percentage of the firm’s total production costs will be spent on good x? (B) Suppose the firm decides to increase its input bundle (x, y) by 10%. That is, it inputs 10% more units of good x and 10%...
Consider the function f(x)=x⋅sin(x). a) Find the area bound by y=f(x) and the x-axis over the...
Consider the function f(x)=x⋅sin(x). a) Find the area bound by y=f(x) and the x-axis over the interval, 0≤x≤π. (Do this without a calculator for practice and give the exact answer.) b) Let M(x) be the Maclaurin polynomial that consists of the first 5 nonzero terms of the Maclaurin series for f(x). Find M(x) by taking advantage of the fact that you already know the Maclaurin series for sin x. M(x)= c) Since every Maclaurin polynomial is by definition centered at...
Consider an economy with the following Cobb–Douglas production function: Y = 4K1/4L3/4. Now suppose that Congress,...
Consider an economy with the following Cobb–Douglas production function: Y = 4K1/4L3/4. Now suppose that Congress, concerned about the welfare of the working class, passes a law setting a minimum wage that is 5 percent above the equilibrium wage you derived in part (b). Assuming that Congress cannot dictate how many workers are hired at the mandated wage, what are the effects of this law? Specifically, calculate what happens to the real wage, employment, output, and the total amount earned...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT