Question

In: Statistics and Probability

4. You own an 8,000 ft^2 (K = 8,000) factory that produces N95 masks and you...

4. You own an 8,000 ft^2 (K = 8,000) factory that produces N95 masks and you produce them by combining labor and capital (your factory) as follows: Q = 4K^(1/3)L^(2/3), where Q is the number of masks produced per week. Assume there are many competing factories and all factories are identical. Until two months ago, the price of masks in this perfectly 1 competitive market was $1.50 each. Today the price is $3.00 ea. The rental value of your factory is $.50 per ft^2/week. Answer the following 2 questions: a)How much profit do you expect to make each week if the price remains at $3.00 ea.? b)If a new identical factory costs $1 million and it is operational within one month, should you purchase it today?

Solutions

Expert Solution

Given production problem :-

where Q is the no. of masks produced per week, K = Capital, L = Labor
(if we compare given production function with generic form, , we get A = 4 and = 1/3)

K = 8000, Rental Cost per week = $ 0.5*8000 = $4000, Rental Rate of Capital = 0.5

(a)
Using formula
Rental Rate of Capital = MPK(Marginal Product of Capital) = = 0.5
i.e. (1/(3*8000))Q = 0.5
So, Q (no. of masks produced) = 12000 per week

Labor Cost = = (2/3)*12000 = $8000

Total Sales/Revenue = $3 * 12000 = $36000
Total Cost = Labor Cost + Rental Cost = $4000 + $8000 = $12000

So, Profit per week = (Revenue - Total Cost) per week = $36000 - $12000 = $24000

(b)
If an identical new factory costs $1million and operational within one month, we will recover our expense in approximately (1+(1000000/(24000*4))) = 11.42 months
So, we should purchase it.

If you have any doubt, feel free to ask in comment box. Please do upvote.


Related Solutions

A trapezoidal tough is 10 ft long, 4 ft wide at the top, 2 ft wide...
A trapezoidal tough is 10 ft long, 4 ft wide at the top, 2 ft wide at the bottom and 2 ft deep. If water flows in the 10 ft^3/ min, find how fast the surface is rising, when the water is 6 in deep. How fast the water surface is rising when the water is 1 foot deep.
You own factory A and factory B. The next cash flow for each factory is expected...
You own factory A and factory B. The next cash flow for each factory is expected in 1 year. Factory A has a cost of capital of 4.3 percent and is expected to produce annual cash flows of $19,100 forever. Factory B is worth $455,000 and is expected to produce annual cash flows of $18,800 forever. Which assertion is true? a. Factory A is more valuable than factory B and factory A is more risky than factory B b. Factory...
Suppose you will receive payments of $8,000, $2,000, and $8,000 in 1, 4, and 9 year(s)...
Suppose you will receive payments of $8,000, $2,000, and $8,000 in 1, 4, and 9 year(s) from now, respectively. What is the total present value of this stream of payments if the interest rate is 9%? Enter your response below rounded to 2 decimal places.
You own factory A and factory B. The next cash flow for eachfactory is expected...
You own factory A and factory B. The next cash flow for each factory is expected in 1 year. Factory A has a cost of capital of 3.5 percent and is expected to produce annual cash flows of $19,300 forever. Factory B is worth $545,000 and is expected to produce annual cash flows of $19,900 forever. Which assertion is true?a.Factory A is more valuable than factory B and factory A is more risky than factory Bb.Factory A is more valuable...
An existing rural 4-lane freeway (2 lanes in each direction) has 11-ft lanes and 2-ft lateral...
An existing rural 4-lane freeway (2 lanes in each direction) has 11-ft lanes and 2-ft lateral clearance. The freeway hasa peak-hour volume of 1,800 veh/h in one direction, 5% trucks in the traffic stream, and a PHF of 0.92. The freeway has 1 cloverleaf interchange within three miles of the midpoint of segment, and runs through level terrain. No recent field speed data is available. a) Using HCS7, determine the LOS during the peak hour. b) What is the capacity...
QUESTION 2 20 MARKS William and Paul own a business selling face masks and hand sanitiser....
QUESTION 2 20 MARKS William and Paul own a business selling face masks and hand sanitiser. They agreed that profits will be spilt 80% to William and 20% to Paul and that losses will be split 50% to each of them. They also agreed that before any profits or losses are split Paul gets a salary and William gets interest on his capital contributions. Paul gets a salary because he spends most of his time in the shop dealing with...
4. You own one Nov. 20 put options contact on Canadian dollar with K = $0.8050...
4. You own one Nov. 20 put options contact on Canadian dollar with K = $0.8050 for which you paid a premium of $0.01/C$. The spot exchange rate today is $0.7900. (i) How would you classify this option today, in-the-money or out-of-the-money? (ii) What is your profit/loss if you sell this option today if it is trading at a premium of $0.015/C$? Contract size is C$100,000 and the U.S. interest rate is 2%. Assume that you bought this option in...
You own a portfolio that has a total value of 118,000 dollars. The portfolio has 8,000...
You own a portfolio that has a total value of 118,000 dollars. The portfolio has 8,000 shares of stock A, which is priced at 9.3 dollars per share and has an expected return of 11.97 percent. The portfolio also has 10,000 shares of stock B, which has an expected return of 15.29 percent. The risk-free return is 4.22 percent and inflation is expected to be 1.98 percent. What is the risk premium for your portfolio? Answer as a rate in...
Suppose you own a factory. You want to determine whether the level of illumination on the...
Suppose you own a factory. You want to determine whether the level of illumination on the assembly line affects worker productivity. One day, you have one group of 5 employees work under very dim lighting, a second group of 5 employees work under a moderate level of light, and a third group of 5 employees work under very bright lights. The mean productivity (number of units assembled) for the low light group was 56; for the moderate light group, 68;...
.  Suppose you own a factory.  You want to determine whether the level of illumination on the assembly...
.  Suppose you own a factory.  You want to determine whether the level of illumination on the assembly line affects worker productivity.  One day, you have one group of 5 employees work under very dim lighting, a second group of 5 employees work under a moderate level of light, and a third group of 5 employees work under very bright lights.  The mean productivity (number of units assembled) for the low light group was 56; for the moderate light group, 68; for the bright...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT