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5. (a) (5 points) A firm produces aln(L 1) units of a commodity when labour input...
2. A firm produces (= units of a commodity when labour input is L units. The...
2. A firm produces (= units of a commodity when labour input is L units. The price obtained per unit of output is P, and the price per unit of labour is w, both positive. (a) Write down the profit function w. What choice of labour input L=L* maximizes profits? (b) Consider L* as a function L (P, w) of the two prices, and define the value function (P, w) = (L* (P, w), P, w) Verify that ax/aP =...
Single Variable Optimization 4. A firm produces Q = 2/L units of a commodity when L...
Single Variable Optimization
4. A firm produces Q = 2/L units of a commodity when L units of labor are employed. If the price obtained per unit is $160 and the price per unit of labor is $40, what value of L maximizes profit?
SM 3. A firm uses capital K, labour L, and land T to produce units of...
SM 3. A firm uses capital K, labour L, and land T to produce units of a commodity, where Q=K2/3+ 1/2+/3 Suppose that the firm is paid a positive price p for each unit it produces, and that the positive prices it pays per unit of capital, labour, and land are r, w, and q, respectively. (a) Express the firm's profits as a function of (K,L,T). Then, find the values of K, L, and T, as functions of the four...
3. Consider a price-taking firm that produces widgets with only labour input. Let the relation between...
3. Consider a price-taking firm that produces widgets with only labour input. Let the relation between widget output and labour input be the function f(n), where n is labour input. Denote the price of widgets by p and the wage rate (the price of labour) by w. "Price taking" means that w and p are beyond the firm's control. Profits are defined to be total revenue less total costs. Write profits as a function of n.p, w: enote the function...
Exercise 2. A Los Angeles firm uses a single input (labor) to produce a recreational commodity...
Exercise 2. A Los Angeles firm uses a single input (labor) to produce a recreational commodity according to a production function Q(L)4VL, where L is the amount of labor it uses. The commodity sells for $100 per unit. The input costs $50 per unit. Write down a function that states the firm's profit as a function of the amount of input. b. What is the profit-maximizing amount of input? What is the profit- maximizing amount of output? How much profit...
2. (3 points) A company produces x units of commodity A and y units of commodity...
2. (3 points) A company produces x units of commodity A and y units of commodity B. All the units can be sold for p = 90 – x dollars per unit of A and q = 60 – y dollars per unit of B. The cost (in dollars) of producing these units is given by the joint-cost function C(x, y) = + 2xy + y? What should x and y be to maximize profit? What is this maximum profit...
(1 point) A company produces x units of commodity A and y units of commodity B...
(1 point) A company produces x units of commodity A and y units of commodity B each hour. The company can sell all of its units when commodity A sels for p-100-8x dollars per unit and commodity B sells for q = 40-10y dollars per unit. The cost (in dollars) of producing these units is given by the joint-cost function C(x, y)-5xy +5. How much of commodity A and commodity B should be sold in order to maximize profit? Commodity...
1. (25 points) A simply supported beam of diameter D, length L, and modulus of elasticity E (units of N/m2)is subjected to a fluid crossflow of velocity V, density p and visosity . Its center deflect...
1. (25 points) A simply supported beam of diameter D, length L, and modulus of elasticity E (units of N/m2)is subjected to a fluid crossflow of velocity V, density p and visosity . Its center deflection δ is assumed to be a function of all these variables. Using p, L and V as the repeating variables for Buckingham's π theorem, determine the dimension!cs parameters that are involved in this relation singp l an
1. (25 points) A simply supported beam...
4. Suppose a firm uses only one input (L) to produce output y, with the production...
4. Suppose a firm uses only one input (L) to produce output y, with the production function y L Suppose the firm sells its output in a competitive market at price p, and buys labor in a competitive market at price w. a. Write an expression for the profits of the firm as a function of w, p, and L. b. What is the marginal cost of hiring an additional unit of labor? Graph the marginal cost of labor curve...
1. Prunella raises peaches. L is the number of units of labour she uses and T is the number of un...
1. Prunella raises peaches. L is the number of units of labour she uses and T is the number of units of land she uses, her output (bushels of peaches), denoted as Q, is given by Q = √ LT . (a) Consider the short-run decision, in which she has a fixed amount of land (T = 9). Does this production function exhibit the diminishing marginal return on the labour input? Explain your answer. (b) If she uses 4 units...
2. A firm produces (= units of a commodity when labour input is L units. The price obtained per unit of output is P, and the price per unit of labour is w, both positive. (a) Write down the profit function w. What choice of labour input L=L* maximizes profits? (b) Consider L* as a function L (P, w) of the two prices, and define the value function (P, w) = (L* (P, w), P, w) Verify that ax/aP =...
Single Variable Optimization
4. A firm produces Q = 2/L units of a commodity when L units of labor are employed. If the price obtained per unit is $160 and the price per unit of labor is $40, what value of L maximizes profit?
SM 3. A firm uses capital K, labour L, and land T to produce units of a commodity, where Q=K2/3+ 1/2+/3 Suppose that the firm is paid a positive price p for each unit it produces, and that the positive prices it pays per unit of capital, labour, and land are r, w, and q, respectively. (a) Express the firm's profits as a function of (K,L,T). Then, find the values of K, L, and T, as functions of the four...
3. Consider a price-taking firm that produces widgets with only labour input. Let the relation between widget output and labour input be the function f(n), where n is labour input. Denote the price of widgets by p and the wage rate (the price of labour) by w. "Price taking" means that w and p are beyond the firm's control. Profits are defined to be total revenue less total costs. Write profits as a function of n.p, w: enote the function...
Exercise 2. A Los Angeles firm uses a single input (labor) to produce a recreational commodity according to a production function Q(L)4VL, where L is the amount of labor it uses. The commodity sells for $100 per unit. The input costs $50 per unit. Write down a function that states the firm's profit as a function of the amount of input. b. What is the profit-maximizing amount of input? What is the profit- maximizing amount of output? How much profit...
2. (3 points) A company produces x units of commodity A and y units of commodity B. All the units can be sold for p = 90 – x dollars per unit of A and q = 60 – y dollars per unit of B. The cost (in dollars) of producing these units is given by the joint-cost function C(x, y) = + 2xy + y? What should x and y be to maximize profit? What is this maximum profit...
(1 point) A company produces x units of commodity A and y units of commodity B each hour. The company can sell all of its units when commodity A sels for p-100-8x dollars per unit and commodity B sells for q = 40-10y dollars per unit. The cost (in dollars) of producing these units is given by the joint-cost function C(x, y)-5xy +5. How much of commodity A and commodity B should be sold in order to maximize profit? Commodity...
1. (25 points) A simply supported beam of diameter D, length L, and modulus of elasticity E (units of N/m2)is subjected to a fluid crossflow of velocity V, density p and visosity . Its center deflection δ is assumed to be a function of all these variables. Using p, L and V as the repeating variables for Buckingham's π theorem, determine the dimension!cs parameters that are involved in this relation singp l an
1. (25 points) A simply supported beam...
4. Suppose a firm uses only one input (L) to produce output y, with the production function y L Suppose the firm sells its output in a competitive market at price p, and buys labor in a competitive market at price w. a. Write an expression for the profits of the firm as a function of w, p, and L. b. What is the marginal cost of hiring an additional unit of labor? Graph the marginal cost of labor curve...
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