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Problem 3. A profit-maximizing firm produces apples, and its production function is (L)- where L is...
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...
1. Suppose that the production function for lava lamps is given by Q = KL -ľ, where is the number of lamps produced pe...
1. Suppose that the production function for lava lamps is given by Q = KL -ľ, where is the number of lamps produced per year, K is the machine-hours of capital, and L is the man-hours of labor. Suppose K = 600. a. Draw a graph of the production function over the range L = 0 to L = 500, putting L on the horizontal axis and on the vertical axis. Over what range of L does the production function...
Consider production function f(l, k) = l2 + k2 (a) Evaluate the returns to scale. (b)...
Consider production function f(l, k) = l2 + k2 (a) Evaluate the returns to scale. (b) Calculate the marginal product of labor and the marginal product of capital. (c) Calculate the MRTS. (d) Does the production function exhibit diminishing MRTS? (e) Plot the isoquant for production level q = 1. Hint: Notice that the input mixes (1; 0) and (0; 1) are on this isoquant.
a. A firm has the production function q = ln L+12L^2- 10L^3. Find the average product...
a. A firm has the production function q = ln L+12L^2- 10L^3. Find the average product of labor, the marginal product of labor. b. Consider the following short-run production function: q = 6L^22 – 1/3L^3. At what level of L do diminishing marginal returns begin? At what level of L do diminishing returns begin?
At its current level of production, a profit-maximizing firm in a competitive market receives $15 for...
At its current level of production, a profit-maximizing firm in a competitive market receives $15 for each unit it produces and faces an average total cost of $10. At the market price of S15 per unit, the firm's marginal cost curve crosses the marginal revenue curve at an output level of 1.300 units. What is the fim's current profit? What is likely to occur in this market and why?
At its current level of production a profit-maximizing firm in a competitive market receives $10 for...
At its current level of production a profit-maximizing firm in a competitive market receives $10 for each unit it produces and faces an average total cost of $12.5. At the market price of $10 per unit, the firm's marginal cost curve crosses the marginal revenue curve at an output level of 1,000 units. What is the firm's current profit? What is likely to occur in this market and why?
, A profit-maximizing monopolist produces electricity. Its cost function is given by C(a)-6q The price of...
, A profit-maximizing monopolist produces electricity. Its cost function is given by C(a)-6q The price of unit electricity is denoted by pe. Suppose that the market demand is given by q 1. Write down the monopolist's profit maximization problem. 2. Draw MC(), MR(a), 3. Determine the optimal levels of production gMand pricePe 4.lustrate that the monopolist price is higher than the competitive equilibrium price and pelin a same figure. PC pe
A monopolist has a production function 27 (L-2)(K+1) Q(L,K) where L, Kis the amount of labor...
A monopolist has a production function 27 (L-2)(K+1) Q(L,K) where L, Kis the amount of labor and capital. The wage rate is denoted by w and the rental rate of capital is denoted by r. The inverse demand function the monopolist is faced with is given by P = 12- 3Q where P is the market price and Q is the quantity sold. 13. Write down the optimization problem of the monopolist. 14. Write down the first order condition(s) 15....
Question 2: Production Function and Profit Maxi- mization Consider a production function of Cobb-Douglas form: for...
Question 2: Production Function and Profit Maxi- mization Consider a production function of Cobb-Douglas form: for some α, β E (0, 1) (a) Plot the isoquant of F (b) Derive that technical rate of substitution of F. Does F exhibit diminishing technical rate of substitution? (c) Does F exhibit diminishing marginal productivity of labor? What about marginal (d) Find out the conditions for α and β such that F is increasing return to scale, (e) Suppose that F does not...
4. A company produces economic analysis reports using hours of labor (L) and computers (K). The...
4. A company produces economic analysis reports using hours of labor (L) and computers (K). The production function is ? = 2?√? Initially, in the short run, they have just 1 computer (K = 1). The wage is $20 per hour, and the cost of capital is $10. a. Derive short run total cost and short run average costs curves, with costs as a function of q. Do these costs curves exhibit economies or diseconomies of scale? Explain. (5) b....
1. Suppose that the production function for lava lamps is given by Q = KL -ľ, where is the number of lamps produced per year, K is the machine-hours of capital, and L is the man-hours of labor. Suppose K = 600. a. Draw a graph of the production function over the range L = 0 to L = 500, putting L on the horizontal axis and on the vertical axis. Over what range of L does the production function...
At its current level of production, a profit-maximizing firm in a competitive market receives $15 for each unit it produces and faces an average total cost of $10. At the market price of S15 per unit, the firm's marginal cost curve crosses the marginal revenue curve at an output level of 1.300 units. What is the fim's current profit? What is likely to occur in this market and why?
, A profit-maximizing monopolist produces electricity. Its cost function is given by C(a)-6q The price of unit electricity is denoted by pe. Suppose that the market demand is given by q 1. Write down the monopolist's profit maximization problem. 2. Draw MC(), MR(a), 3. Determine the optimal levels of production gMand pricePe 4.lustrate that the monopolist price is higher than the competitive equilibrium price and pelin a same figure. PC pe
A monopolist has a production function 27 (L-2)(K+1) Q(L,K) where L, Kis the amount of labor and capital. The wage rate is denoted by w and the rental rate of capital is denoted by r. The inverse demand function the monopolist is faced with is given by P = 12- 3Q where P is the market price and Q is the quantity sold. 13. Write down the optimization problem of the monopolist. 14. Write down the first order condition(s) 15....
Question 2: Production Function and Profit Maxi- mization Consider a production function of Cobb-Douglas form: for some α, β E (0, 1) (a) Plot the isoquant of F (b) Derive that technical rate of substitution of F. Does F exhibit diminishing technical rate of substitution? (c) Does F exhibit diminishing marginal productivity of labor? What about marginal (d) Find out the conditions for α and β such that F is increasing return to scale, (e) Suppose that F does not...
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