Question

2.   Bridgestone Company has the following production function for tires: Q = 20 K 0.2 L...

2.   Bridgestone Company has the following production function for tires: Q = 20 K 0.2 L 0.8, where K represents machine hours and L represents labor hours. They pay $ 15 per hour to rent their machines and $ 10 per hour to their workers. They have $ 12,000 to spend on capital and labor.

A. Does this production function exhibit constant, increasing, or decreasing returns to scale?

B. Does this production function exhibit diminishing marginal returns to capital and labor?

C. Derive the optimal bundle of capital and labor to achieve the desired level of output. What is the maximum amount of output that they can produce with this $ 12,000 in expenditures?

Homework Answers

Answer #1

A. Production function exhibits constant returns to scale.

Since the production function is a Cobb Douglas production function.

a+b=1 as 0.2+0.8=1, So the production function is a constant returns to scale.

B. Marginal product of capital= 0.2*20* k^-0.8 * L^0.8

Marginal product of labor= 0.8*20* K^0.2* L^-0.2

Marginal product diminishes as Capital increases and marginal product diminishes as labor increases.

So this function exhibits diminishing Returns in Capital and labor.

c. MRTS= 4k/L

At equilibrium , MRTS= r/w=15/10=1.5

L=6K

12000= wk+rL

12000=15k+10*6k

12000=75k

k*= 160

L*= 960

Q=20* (160)^0.2 (960)^0.8

Q= 13419.1

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Wheat is produced according to the production function Q = 100 K^0.8 L^0.2 a. Beginning with...
Wheat is produced according to the production function Q = 100 K^0.8 L^0.2 a. Beginning with a capital input of 4 and a labor input of 49, show that the marginal product of labor and the marginal product of capital are both decreasing. b. Does this production function exhibit increasing, decreasing, or constant returns to scale? please explain in 4 sentences thank you!
2. A firm has the following linear production function: q = 5L + 2K a. Does...
2. A firm has the following linear production function: q = 5L + 2K a. Does this firm’s production function exhibit diminishing returns to labor?    b. Does this production function exhibit diminishing returns to capital? c. Graph the isoquant associated with q = 20. d. What is the firm’s MRTS between K and L? e. Does this production technology exhibit decreasing, constant, or increasing returns to scale?
The production function for the Roundtree Laser Company is: Q=(10L^.5)(K^.3)(M^.3) where: Q: number of lasers produced...
The production function for the Roundtree Laser Company is: Q=(10L^.5)(K^.3)(M^.3) where: Q: number of lasers produced per week L: amount of labor used per week K: the amount of capital used per week M: quantity of raw materials used per week a) Does the production function exhibit decreasing returns to scale? b) Does the production function exhibit diminishing marginal returns?
Suppose a firm’s long-run production function is given by Q=K^0.25 L^0.25 ,where K is measured in...
Suppose a firm’s long-run production function is given by Q=K^0.25 L^0.25 ,where K is measured in machine-hours per year and L is measured in hours of labor per year. The cost of capital (rental rate denoted by r) is $1200 per machine-hour and the cost of labor (wage rate denoted by w) is $12 per hour. Hint: if you don’t calculate the exponential terms (or keep all the decimals when you do), you will end up with nice numbers on...
A firm’s production function is given by Q = 5K1/3 + 10L1/3, where K and L...
A firm’s production function is given by Q = 5K1/3 + 10L1/3, where K and L denote quantities of capital and labor, respectively. Derive expressions (formulas) for the marginal product of each input. Does more of each input increase output? Does each input exhibit diminishing marginal returns? Prove. Derive an expression for the marginal rate of technical substitution (MRTS) of labor for capital. Suppose the price of capital, r = 1, and the price of labor, w = 1.   The...
Suppose a competitive firm’s production function is Y= 20 L1/2 K1/3. L is Labor , K...
Suppose a competitive firm’s production function is Y= 20 L1/2 K1/3. L is Labor , K is capital and Y is output. a) (4) Find the marginal product of labor and capital. b) (4) What is Marginal Rate of technical Substitution of Labor for Capital? c) (2) Does this production function exhibit increasing, decreasing or constant returns to scale? Show your work.
1. Consider the following production function: Y=F(A,L,K)=A(K^α)(L^(1-α)) where α < 1. a. Derive the Marginal Product...
1. Consider the following production function: Y=F(A,L,K)=A(K^α)(L^(1-α)) where α < 1. a. Derive the Marginal Product of Labor(MPL). b. Show that this production function exhibit diminishing MPL. c. Derive the Marginal Production of Technology (MPA). d. Does this production function exhibit diminishing MPA? Prove or disprove
Joe’s coffee house operates under the production function Q =2√? + ?^2/3, where L is the...
Joe’s coffee house operates under the production function Q =2√? + ?^2/3, where L is the number of worker hours and K is the number of coffee machine hours. a. Clearly show what type of returns to scale is exhibited. b. Does labor exhibit diminishing marginal returns when capital is fixed? Explain.
A firm produces output according to the production function. Q=sqrt(L*K) The associated marginal products are MPL...
A firm produces output according to the production function. Q=sqrt(L*K) The associated marginal products are MPL = .5*sqrt(K/L) and MPK = .5*sqrt(L/K) (a) Does this production function have increasing, decreasing, or constant marginal returns to labor? (b) Does this production function have increasing, decreasing or constant returns to scale? (c) Find the firm's short-run total cost function when K=16. The price of labor is w and the price of capital is r. (d) Find the firm's long-run total cost function...
An electronics plant’s production function is Q = L 2K, where Q is its output rate,...
An electronics plant’s production function is Q = L 2K, where Q is its output rate, L is the amount of labour it uses per period, and K is the amount of capital it uses per period. (a) Calculate the marginal product of labour (MPL) and the marginal product of capital (MPK) for this production function. Hint: MPK = dQ/dK. When taking the derivative with respect to K, treat L as constant. For example when Q = L 3K2 ,...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT