1. [Multi-product Firm’s Profit Maximization] Find (i) the profit maximizing output levels x and y and...
1. [Multi-product Firm’s Profit Maximization]
Find (i) the profit maximizing output levels x and y and (ii) the maximum profit for a firm producing two goods x and y with the profit function
π(x, y) = 86x−2x2 −2xy−4y2 +120y−200.
Homework Answers
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1. [Multi-product Firm’s Profit Maximization]
Find (i) the profit maximizing output levels x and y and...
A price-taking and profit-maximizing firm produces one output at the rate y> 0 using one input...
A price-taking and profit-maximizing firm produces one output at the rate y> 0 using one input r>0 by way of the production function () , where f(x)竺2x2 . The firm's output sells at the price p >0 while the input is purchased at the price wo (a) (b) (c) Determine the lalue of the input that solves the FONC, and denote it by x (p,w). Is Set up the profit maximization problem. Derive the FONC and SOSC. x(p,w) unique? Explain....
1.1. What is the set of profit-maximizing inputs if the profit function of a firm is...
1.1. What is the set of profit-maximizing inputs if the profit function of a firm is given by: π(X, Y) = P ln[X + aY] – wX – wY where P - price of output f(X,Y) = ln[X + 0.5Y] - production function X - input 1, X>=0 Y - input 2, Y>=0 w - same price of input for inputs 1 and 2 a - parameter between 0 and 1 1.2 What is the set of profit-maximizing inputs if...
Suppose the short run cost function for a competitive firm is C(Y)= 4Y2+ 200 where Y...
Suppose the short run cost function for a competitive firm is C(Y)= 4Y2+ 200 where Y is the total output. Find the profit maximizing supply for the firm if the output price is $16 and the maximum profit. What is its short run decision: To produce or not to produce?
Consider a profit maximizing firm that uses a Cobb-Douglas production function Y = AKαL 1−α and...
Consider a profit maximizing firm that uses a Cobb-Douglas production function Y = AKαL 1−α and hires labor L at wage rate w and capital K at rental rate r. (1) Set up the profit-maximization problem of the firm and derive the first-order condition for the profit-maximizing choice of capital. (2) Show that the marginal product of capital is a decreasing function of capital. (3) Solve for the optimal choice of capital and show that the optimal choice of capital...
B. A firm produces and sells two commodities. By selling x tons of the first commodity...
B. A firm produces and sells two commodities. By selling x tons of the first commodity the firm gets a price per ton given by p = 96 – 4x. By selling y tons of the other commodity the price per ton is given by q = 84 – 2y. The total cost of producing and selling x tons of the first commodity and y tons of the second is given by C(x, y) = 2x2 + 2xy + y2....
5. Suppose that a firm's total profit function is P(x,y) = 2xy + 2y+12-(2x2 +y2), where...
5. Suppose that a firm's total profit function is P(x,y) = 2xy + 2y+12-(2x2 +y2), where x is amount of production and sales of the first product and y - of the second produc 1) Find all first and second order partial derivatives. 2) Find values of x and y that maximize the profit. Find the maximum profit. 6. Ifx thousand euros is spend on labor and y thousand euros is spend on equipment, the outpu certain factory will be...
3. Consider a firm with the production function F(KL)=1/31/3 You will be solving the profit maximization...
3. Consider a firm with the production function F(KL)=1/31/3 You will be solving the profit maximization for this firm with both the two step and I step methods and proving that the final answers are identical. This big problem is broken up into the following smaller parts: (a) Setup and solve the long run cost minimization problem for the long run optimal amount of capital K*(w,,9) and labor L*(w,r.9), and the long run minimized cost C*(w, 5,9). (Hint: reduce the...
Problem 3 - Profit Maximization Consider the case of a firm that produces output x (sold...
Problem 3 - Profit Maximization Consider the case of a firm that produces output x (sold at price p) using a production function x = A*1941-a-Beß, where lis labor, k is capital, and e is energy (for example, oil or electricity). a) What is the interpretation of A? b) Under what condition(s) does the production function exhibit constant returns to scale? Is it homogeneous? Are the marginal products of inputs increasing, constant, or decreasing? c) Set up the profit maximization...
1. If a profit-maximizing competitive firm has constant returns to scale, then its long-run profits must...
1. If a profit-maximizing competitive firm has constant returns to scale, then its long-run profits must be zero. True or False? Explain your answer. 2. A firm is producing output using one variable factor of production. The firm’s production function is y = 8x¹ˡ². The price of the output is $24 and the price of input is $8 per unit. How many units of the input should the firm use?
A competitive firm uses a single input x to produce its output y. The firm’s production...
A competitive firm uses a single input x to produce its output y. The firm’s production function is given by y = x3/2 for quantities of x between 0 and 4. For quantities of a greater than 4, the firm’s output is y = 4 + x. If the price of the output y is $1 and the price of the input x is $3, how much x should the firm use to maximize its profit? answer is 0.
A price-taking and profit-maximizing firm produces one output at the rate y> 0 using one input r>0 by way of the production function () , where f(x)竺2x2 . The firm's output sells at the price p >0 while the input is purchased at the price wo (a) (b) (c) Determine the lalue of the input that solves the FONC, and denote it by x (p,w). Is Set up the profit maximization problem. Derive the FONC and SOSC. x(p,w) unique? Explain....
B. A firm produces and sells two commodities. By selling x tons of the first commodity the firm gets a price per ton given by p = 96 – 4x. By selling y tons of the other commodity the price per ton is given by q = 84 – 2y. The total cost of producing and selling x tons of the first commodity and y tons of the second is given by C(x, y) = 2x2 + 2xy + y2....
5. Suppose that a firm's total profit function is P(x,y) = 2xy + 2y+12-(2x2 +y2), where x is amount of production and sales of the first product and y - of the second produc 1) Find all first and second order partial derivatives. 2) Find values of x and y that maximize the profit. Find the maximum profit. 6. Ifx thousand euros is spend on labor and y thousand euros is spend on equipment, the outpu certain factory will be...
3. Consider a firm with the production function F(KL)=1/31/3 You will be solving the profit maximization for this firm with both the two step and I step methods and proving that the final answers are identical. This big problem is broken up into the following smaller parts: (a) Setup and solve the long run cost minimization problem for the long run optimal amount of capital K*(w,,9) and labor L*(w,r.9), and the long run minimized cost C*(w, 5,9). (Hint: reduce the...
Problem 3 - Profit Maximization Consider the case of a firm that produces output x (sold at price p) using a production function x = A*1941-a-Beß, where lis labor, k is capital, and e is energy (for example, oil or electricity). a) What is the interpretation of A? b) Under what condition(s) does the production function exhibit constant returns to scale? Is it homogeneous? Are the marginal products of inputs increasing, constant, or decreasing? c) Set up the profit maximization...
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