Question

In: Economics

(show all your work and calculations) A certain production process employs two inputs¾labor (L) and raw...

(show all your work and calculations)

A certain production process employs two inputs¾labor (L) and raw materials (R).  Output (Q) is a function of these two inputs and is given by the following relationship:

                           Q = 6L2 R2 - 0.1L3 R3

Assume that raw materials (input R) are fixed at 10 units

5 - Find the number of units of input L that maximizes the marginal product function

6 - Find the number of units of input L that maximizes the average product function

7 - Determine the boundaries for the three stages of production

8 - Find the number of units of input L where the law of Diminishing Marginal Returns starts to take effect first

Solutions

Expert Solution


Related Solutions

Consider a production function of two inputs, labor and capital, given by Q = (√L +...
Consider a production function of two inputs, labor and capital, given by Q = (√L + √K)2. Let w = 2 and r = 1. The marginal products associated with this production function are as follows:MPL=(√L + √K)L-1/2MPK=(√L + √K)K-1/2 a) Suppose the firm is required to produce Q units of output. Show how the cost-minimizing quantity of labor depends on the quantity Q. Show how the cost-minimizing quantity of capital depends on the quantity Q. b) Find the equation...
Suppose there are two inputs in the production function, labor and capital, and these two inputs...
Suppose there are two inputs in the production function, labor and capital, and these two inputs are perfect substitutes. The existing technology permits 5 machines to do the work of 2 workers. So the production function is f(E, K) = 2K + 5E. The firm wants to produce q units of output, where q > 0 is some number. Suppose the price of capital is $10 per machine per hour. What combination of inputs will the firm use if the...
Capital and labor are the only two inputs for the following production process. Capital is fixed...
Capital and labor are the only two inputs for the following production process. Capital is fixed at 4 units, which costs 50 dollars each unit per day. Workers can be hired for 100 each per day. Complete the following table and plot the marginal cost (MC), average total cost (ATC), average variable cost (AVC), average fixed cost (AFC) on the same graph. The quantity of labor input Total output per day AFC AVC ATC MC    0 0 1 100...
Show all of your work in the space provided. Show all of your work to get...
Show all of your work in the space provided. Show all of your work to get full credit. All answers have to be in SI units(20 pints for each questions). 2.Following are the two sets of position and time data collected using a motion sensor and cart.        Table 1. table 2 Time (s) Position (m) V(instantaneous) (m/s) 0 10.0 0.25 13.0 0.50 16.5 0.75 21.0 1.00 26.5 1.25 32.3 1.50 38.0 1.75 44.5 2.00 52.0 2.25 60.0 2.50 68.5...
Show your work. Carry out all calculations to at least 3 significant digits. A manufacturer of...
Show your work. Carry out all calculations to at least 3 significant digits. A manufacturer of TV sets claims that at least98% of its TV sets can last more than10years without needing a single repair. In order to verify and challenge this claim, a consumer group randomly selected 800 consumers who had owned a TV set made by this manufacturer for 10 years. Of these 800 consumers, 60 said that their TV sets needed some repair at least once. a....
Suppose there are two inputs in the production function, labor and capital, which are substitutes. The...
Suppose there are two inputs in the production function, labor and capital, which are substitutes. The current wage is $10 per hour and the current price of capital is $25 per hour. Given the following information on the marginal product of labor and the marginal product of capital, find the firm’s profit-maximizing input mix (i.e. number of workers and units of capital) in the long-run. Show your work and explain. L MPL K MPK 1 125 1 130 2 100...
PLEASE SHOW ALL WORK IN EXCEL!!!!!!! SHOW CALCULATIONS / FORMULAS IN EXCEL!!!!!!!! Voters arrive at a...
PLEASE SHOW ALL WORK IN EXCEL!!!!!!! SHOW CALCULATIONS / FORMULAS IN EXCEL!!!!!!!! Voters arrive at a polling station at an average of 4 per minute (Poisson) where the service rate is 50 per hour (Poisson). a. What is the average number of voters in the system with 5 voter booths? (10 pts) b. What is the minimum number of voting booths needed to keep the average time in the system under three minutes? (10 pts) PLEASE SHOW ALL WORK IN...
Show all work and calculations In a mixture of argon and hydrogen, occupying a volume of...
Show all work and calculations In a mixture of argon and hydrogen, occupying a volume of 1.18 L at 894.6 mmHg and 44.1oC, it is found that the total mass of the sample is 1.25 g. What is the partial pressure of argon? A 18.8-g mixture of nitrogen and carbon dioxide is found to occupy a volume of 13.5 L when measured at 759.1 mmHg and 25.6oC. What is the mole fraction of carbon dioxide in this mixture?
Please complete the following problems. Please explain and show your work for all calculations: You intend...
Please complete the following problems. Please explain and show your work for all calculations: You intend to purchase a 10-year, $1,000 face value bond that pays interest of $60 every six months. If the yield to maturity is 10% with semiannual compounding, how much should you be willing to pay for this bond? A ten year bond with a coupon rate of 12% (payable annually) and a face value of $1,000 is selling for $1,192.50 today. What is the bond’s...
A firm uses two inputs in production: capital and labor. In the short run, the firm...
A firm uses two inputs in production: capital and labor. In the short run, the firm cannot adjust the amount of capital it is using, but it can adjust the size of its workforce. -- If the cost of renting capital increases, which of the following curves will be affected? (Check all answers that apply). -- Average variable cost Marginal cost Average fixed cost Average total cost 2 points    QUESTION 2 If the cost of hiring workers increases, which...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT