A firm’s production function is y = f(x1, x2) = a1 ln x1 + a2 ln...
A firm’s production function is y = f(x1, x2) = a1 ln x1 + a2 ln x2, where ai > 0. Find the factor demand, supply, and profit functions. Apply Hotelling’s lemma after finding the profit function.
Homework Answers
A firm’s production function is f(x1, x2) = min{x1, x2} a What restriction must a satisfy...
A firm’s production function is f(x1, x2) = min{x1, x2} a What restriction must a satisfy in order for profits to be maximised? Find the factor demand, supply, and the profit functions.
Suppose that a firm has the production function (1) Draw an isoquant for f(x1,x2) = 10....
Suppose that a firm has the production function (1) Draw an isoquant for f(x1,x2) = 10. (5 points) (w1, w2) respec- (2) Suppose that the price of product is p, and that the prices of factors are tively. Find the factor demand function ri(w, w2, p), x1(w1, w2, P), the supply function y(w1, W2, P), and the profit function T(w1, w2, p). (10 points)
Suppose that a firm has the production function (1) Draw an isoquant for f(x1,x2) = 10....
A firm uses two inputs x1 and x2 to produce output y. The production function is...
A firm uses two inputs x1 and x2 to produce output y. The production function is f(x1, x2) = x11/2 + x21/2. The price of input 1 is 1 and the price of input 2 is 2. The price of output is 10. (d) Does this production function exhibit increasing, decreasing or constant returns to scale? (e) Solve the firm’s cost minimization problem. Derive the firm’s cost function c(y). (f) Find the profit-maximizing choice of inputs x1* and x2* and...
A competitive firm’s production function is f(x1, x2) = 6x1/21 + 8x1/22. The price of factor...
A competitive firm’s production function is f(x1, x2) = 6x1/21 + 8x1/22. The price of factor 1 is $1 and the price of factor 2 is $4. The price of output is $8. What is the profit-maximizing quantity of output? a. 416 b. 208 c. 204 d. 419 e. 196
An individual has the utility function: U(x1,x2,x3) = ln x1 + ln x2 + 0.5ln x3....
An individual has the utility function: U(x1,x2,x3) = ln x1 + ln x2 + 0.5ln x3. The price of good x1 is p1, the price of good x2 is p2 = 1 and the price of good x3 is p3. The individual’s income is I. Derive the Marshallian demand functions (x1* , x2*, x3* ).
Problem 2: A firm has the following production function: f(x1,x2) = x1 + x2 A) Does...
Problem 2: A firm has the following production function: f(x1,x2) = x1 + x2 A) Does this firm's technology exhibit constant, increasing, or decreasing returns to scale? B) Suppose the firm wants to produce exactly y units and that input 1 costs $w1 per unit and input 2 costs $w2 per unit. What are the firm's conditional input demand functions? C) Write down the formula for the firm's total cost function as a function of w1, W2, and y.
A producer produces good y using inputs x1 and x2 according to the production function y...
A producer produces good y using inputs x1 and x2 according to
the production function y = xα1xβ2 where α+β < 1. The factor
prices are w1 and w2 (for input 1 and 2). The producer can sell as
much as he wants at unit price p.
A producer produces good y using inputs X1 and 22 according to the production function y = xqx, where a + B < 1. The factor prices are wi and W2 (for input...
uestion 3 (1 point) the production function is f(x1, x2) = x1/21x1/22. If the price of...
uestion 3 (1 point) the production function is f(x1, x2) = x1/21x1/22. If the price of factor 1 is $10 and the price of factor 2 is $20, in what proportions should the firm use factors 1 and 2 if it wants to maximize profits? Question 3 options: We can’t tell without knowing the price of output. x1 = 2x2. x1 = 0.50x2. x1 = x2. x1 = 20x2. Question 4 (1 point) A firm has the production function f(X,...
a profit maximizing firm has a technology with the production function f(x1,x2) =x1^0.5 x2^0.5 can only...
a profit maximizing firm has a technology with the production function f(x1,x2) =x1^0.5 x2^0.5 can only use 4 units of x2 in the short run. what is the optimal amount of x1 to use in the short run if the price of x1 is $1 and price of output is $13 .how much output does the firm make ? sketch 2 isoquants on same axis for production function f(x,y) = min (y,x^2)
A firm uses two inputs x1 and x2 to produce output y. The production function is...
A firm uses two inputs x1 and x2 to produce
output y. The production function is given by f(x1, x2) = p
min{2x1, x2}. The price of input 1 is 1 and the price of input 2 is
2. The price of output is 10.
4. A firm uses two inputs 21 and 22 to produce output y. The production function is given by f(x1, x2) = V min{2x1, x2}. The price of input 1 is 1 and the price...
Suppose that a firm has the production function (1) Draw an isoquant for f(x1,x2) = 10. (5 points) (w1, w2) respec- (2) Suppose that the price of product is p, and that the prices of factors are tively. Find the factor demand function ri(w, w2, p), x1(w1, w2, P), the supply function y(w1, W2, P), and the profit function T(w1, w2, p). (10 points)
Suppose that a firm has the production function (1) Draw an isoquant for f(x1,x2) = 10....
Problem 2: A firm has the following production function: f(x1,x2) = x1 + x2 A) Does this firm's technology exhibit constant, increasing, or decreasing returns to scale? B) Suppose the firm wants to produce exactly y units and that input 1 costs $w1 per unit and input 2 costs $w2 per unit. What are the firm's conditional input demand functions? C) Write down the formula for the firm's total cost function as a function of w1, W2, and y.
A producer produces good y using inputs x1 and x2 according to
the production function y = xα1xβ2 where α+β < 1. The factor
prices are w1 and w2 (for input 1 and 2). The producer can sell as
much as he wants at unit price p.
A producer produces good y using inputs X1 and 22 according to the production function y = xqx, where a + B < 1. The factor prices are wi and W2 (for input...
A firm uses two inputs x1 and x2 to produce
output y. The production function is given by f(x1, x2) = p
min{2x1, x2}. The price of input 1 is 1 and the price of input 2 is
2. The price of output is 10.
4. A firm uses two inputs 21 and 22 to produce output y. The production function is given by f(x1, x2) = V min{2x1, x2}. The price of input 1 is 1 and the price...
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