dbebitSuppose a Cobb-Douglas Production function is given by the following:P(L, K)= 40L0.84 K 0.16where L is units of labor, K is units of capital, and P(L, K) is total units that can be produced with thislabor/capital combination. Suppose each unit of labor costs $1,000 and each unit of capital costs $5,000.Further suppose a total of $625,000 is available to be invested in labor and capital (combined).A) How many units of labor and capital should be "purchased" to maximize production subject to yourbudgetary constraint?Units of labor, L-Units of capital, K =B) What is the maximum number of units of production under the given budgetary conditions? (Round youranswer to the nearest whole unit.)Max production =Question Help: Video Message instructorSubmit Questionunits

Each unit of labor cost and each unit of capital cost Total investment

Answered: Suppose a Cobb-Douglas Production…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

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4. At Wally Motors, an auto engineer, in testing a new engine on one of its new models, found that the efficiency e of the engine as a function of the speed s of the car was given by e = 0.768s – 0.00004s. Here e is measured in percent and s is measured in km/hr. What is the maximum efficiency of the engine?
Q. 1. Use production function q(L, K) = L3 K and derive the followings: (a) (b) (c) (d) Short-run and long-run profit functions Short-run and long-run cost functions Short-run and long-run supply function using Hotelling's lemma. Short-run and long-run supply function using Shephard's lemma.
(3) A company manufacturing laundry sinks has fixed costs of $100 per day but has totalcosts of $2,500 per day when producing 15 sinks. The company has a daily demand functionof q = 360 − p, where q is the number if laundry sinks demanded and p is te price ofa laundry sink. (a) If we assume that the total cost per day is linearly related to the amount of sinksproduced in a day, derive the total cost function of the company? (b) Find a function for the average cost of this company. (c) If production increases continuously, what is likely to be the average cost per sink? (d) How many laundry sinks will the company need to produce in order to maximise it′s profits? (e) What is the maximum profit?
(3) A company manufacturing laundry sinks has fixed costs of $100 per day but has total costs of $2,500 per day when producing 15 sinks. The company has a daily demand function of q = 360 – p. where q is the number if laundry sinks demanded and p is te price of a laundry sink. (a) If we assume that the total cost per day is linearly related to the amount of sinks produced in a day, derive the total cost function of the company? (b) Find a function for the average cost of this company. (c) If production increases continuously, what is likely to be the average cost per sink?
3. Prove that if the more general form of the Cobb-Douglas production function Y = AK" L exhibits constant returns to scale then B = 1- a.
Suppose the price elasticity of demand for a given product is E = 9-2p Moreover, the current price is set at p = 3. Which of the following is TRUE? O Price should be increased in order to maximize revenue. Price should be decreased in order to maximize revenue. Revenue is already maximized at the current price. O Increasing or decreasing price will have no effect on revenue. O It cannot be determined what effect increasing or decreasing price will have on revenue.
The hourly cost function (in dollars) of 3 generators, each as follows: where x₁ is the output power of the first generator, x₂ is the output power of the second generator, and x3, is the output power of the third generator. It is known that the three generators serve a load (total output power) of 744 megawatts. Determine the distribution of power that must be generated by each generator so that it can meet the needs load with minimum total operating costs.
II) A firms production is represented by the following Cobb-Douglas function: Q = K13 L23. The rental rate, r, of capital is given by $16 and the price of labor is $4. a. For a given level of output, what should be the ratio of capital to labor in order to minimizecosts?b. How much capital and labor should be used to produce those 200 units?c. What is the minimum cost of producing 200 units?d. What is the additional cost of increasing output to 350 units in the short run and in the longrun?e. Does this production function exhibit increasing, decreasing, or constant returns to scale?Please answer based on the cost calculations in parts c and d.

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