The Director of Jonat Enterprise hires labour (L) and rents capital equipment (K) in a competitive market to produce chocolate pellets. At the moment, the wage rate of labour is GH¢2 per hour and capital is rented at GH¢5 per hour. Also, the unit price of chocolate pellets is GH¢0.75 and total cost of production is GHe 1,000. Suppose the firm's production function (Q) follows a Cobb-Douglas specification given as: Q = 14K0.5 10.5 + 10 Page 3 of 4

The Director of Jonat Enterprise hires labour (L) and rents capital equipment (K) in a competitive market to produce chocolate pellets. At the moment, the wage rate of labour is GH¢2 per hour and capital is rented at GH¢5 per hour. Also, the unit price of chocolate pellets is GH¢0.75 and total cost of production is GHe 1,000. Suppose the firm's production function (Q) follows a Cobb-Douglas specification given as: Q = 14K0.5 10.5 + 10 Page 3 of 4

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

The Director of ABC Enterprise hires labour (L) and rents capital equipment (K) in a competitive market to produce mango juice. At the moment, the wage rate of labour is GH¢2 per hour and capital is rented at GH¢5 per hour. Also, the unit price of mango juice is GH¢0.75 and total cost of production is GH¢1,000. Suppose the firm’s production function (Q) follows a Cobb-Douglas specification given as: 0.5 0.5 ?=14? ? +10 Determine the optimal input usage and the maximum profit that ABC Enterprise would obtain at the optimal input levels.
Subpart 1-3
Please no written by hand The estimated production function is Q = 12K ½ L1/4 The firm pays workers (L) and rents boats (K) in order to produce fish. Currently, the company has no fixed inputs and pays $12 per hour for labour (w) and $16 per hour for capital (r). The quantity of fish produced per day (Q) is 153. A. Derive the conditional input demand functions for labour (L) and capital (K) for IFC. B. What is cost-minimizing amount of labour and capital that IFC should hire and rent? C. Determine the minimum cost of producing 153 units of output? D. Use the isocost and isoquant to illustrate the optimal choice of this firm.
A firm has the following production function: q = 8KL, where q is the weekly output, K is the number of machines and L is the number of workers. Each machine rents for $50,000 per week and each worker costs $2,000 per week. The total cost includes the cost of machines and labor, as well as an additional $5,000 per unit of output for raw materials. The firm currently runs a single factory with 10 machines. Assume that capital is fixed in the short run. (a) How many workers are needed to produce 2,000 units of output per week (in the short run)? (b) How much does it cost to produce q units of output per week (in the short-run)? [The answer I expect is a particular function of q.
Assume the following production function: q = √k + √la) Determine the cost function and the contingent input demand functions. b) If the firm’s output target is 1000 units and the prices per unit of capital and labour are 30 and 10, respectively, what will the firm’s cost be? What will its demand for capital and labour, respectively, be? c) Determine the rate of technical substitution and sketch the isoquant map corresponding to the production function.
1.) A firm engaged in the manufacture of RTWS faces the short-run production function Q = 250L - 5L², where L is the number of units of labor and Q is the number of RTWs produced annually. a.) How many units of labor are needed to maximize production output? b.) Find the maximum number of RTWs that can be produced by the firm in a year. c.) Compute the marginal product of the 10th unit of labor. d.) How many RTWS can be produced by the firm in a year if there are 10 units of labor? e.) Compute the marginal product of the 40th unit of labor. f.) How many RTWs can be produced by the firm in a year if there are 40 units of labor? g.) Sketch the graph of the production function.
A firm produces basketballs with two variable inputs - labour (L) and plastic (K) - and has the following production function: f (L , K) = 6L1/3K1/6 If the price of output is 4, the price of labour is $2 and the price of plastic is $3, calculate the a) profit-maximizing level of each input b) the total production and c) the profit.
4.
A firm can manufacture a product according to the production function Q = F(K, L) = KO.SL0.5. (a) What is the average product of labor, AP, when the level of capital is fixed at 36 units and the firm uses 16 units of labor? (b) What is the marginal product of labor, MP, when capital is fixed at 36 units?
A firm's short-run production function is displayed in the figure below. The firm's variable input is labor. Assume that when Əq (L) 4 units of labor are being used, the slope of the short-run production function reaches its maximum value of 7 (i.e. ƏL 7 when L = 4). As the level of labor increases beyond L = 4, the short-run production function is always becoming less Əq (L) steep (i.e. it is concave). The slope of the production function is equal to 5 when L = 5 (i.e. = 5 when L = 5). If 6 units ƏL Əq (L) of labor are being used, the slope of the production function is 3 (i.e. = 3 when L = 6). If the firm has to pay a wage ƏL of $15 (w = 15) for each unit of labor and can sell each unit of output at a price of $3 (p = 3), what is the firm's profit- maximizing level of output (q) in the short-run? 9₁ 18 14 8 0 4 5 6 q(L) L 7 / 8
A baker uses labor (L) and raw materials (M) to produce mini Muhlenberg Mule sugar figurines (q). The process is fairly simple as workers only must make the sugar mixture and pour the mixture into the mule molds. The baker’s production function is as follows f(L, M) = L 0.50M. Let wL and wM denote the prices of a unit of L and M, respectively. (a) Write the firm’s cost minimization problem if it wants to produce q units of output. (b) Write the Lagrangian function that describes the cost minimization problem. (c) Derive the long run conditional factor input demands for L and M as a function of wL, wM, and q; L ∗ (wL, wM, q) and M∗ (wL, wM, q). (d) Suppose wL = $25 and wM = $2. Determine the cost-minimizing combination of inputs if the baker wants to produce 200 mules. (e) Using wL = $25 and wM = $2 and the demand functions from part (c), write the firm’s long run cost function CLR(q).
Ten-year old Sarah is starting a lemonade stand, she uses baskets of lemons (L) and other ingredients (O). She is able to produce lemonade according to the production function f(L, O) = 1 2 L 2O. The cost of a basket of lemons is $10 and the average cost of the other goods is $4. (a) Derive MPL and MPO. (b) Currently Sarah is using 4 baskets of lemons and 40 units of the other goods. Using this information, calculate MPL and MPO. (c) True/False. At her current use of inputs Sarah is minimizing costs. If true, explain why. If false, what would you recommend Sarah do? (d) Sarah wants to produce 320 units of lemonade. Determine the cost minimizing combination of inputs to use. (e) Assuming no changes in the market price of lemonade nor in the prices of the inputs, if Sarah continues to produce 320 units of lemonade in the long run, what will Sarah’s long run costs be.