Question

A firm uses the inputs of fertilizer, labor, and hothouses to produce roses. Suppose thatwhen the...

A firm uses the inputs of fertilizer, labor, and hothouses to produce roses. Suppose thatwhen the quantity of labor and hothouses is fixed, the relationship between the quantity offertilizer and the number of roses produced is given by the following table:

Tons of fertilizer / month No of roses/ month Tons of fertilizer / month No of roses/ month
0 0 5 2500
1 500 6 2600
2 100 7 2500
3 1700 8 2000
4 2200 - -

(Hint, write out the average and marginal product for each ton of fertilizer)
1. What is the average product of fertilizer when 4 tons are used? (2m)
2. What is the marginal product of the sixth ton of fertilizer? (2m)
3. Does this total product function exhibit diminishing marginal returns? If so, over
what quantities of fertilizer is it diminishing?
4. What is the efficient level of output it must produce at?  

Business   Economics   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

APL = Q / L

MPL = Change in Q / Change in L

L Q APL MPL
0 0
1 500 500 500
2 1000 500 500
3 1700 566.67 1200
4 2200 550 1000
5 2500 500 1500
6 2600 433.33 1100
7 2500 357.14 1400
8 2000 250 600

(1)

When L = 4, APL = 550

(2)

When L = 6, MPL = 1100

(3)

Starting 6th ton of fertilizer, MPL is decreasing with increase in L. So diminishing returns occurs from 6th ton of fertilizer.

(4)

Production is efficient when MPL is maximized (= 1500) and Q = 2500.

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A firm uses the inputs of fertilizer and labor to produce roses. Suppose that when the...
A firm uses the inputs of fertilizer and labor to produce roses. Suppose that when the quantity of labor is fixed, the relationship between the quantity of fertilizer and the number of roses produced is given by the following table: Fertilizer 1 2 3 4 5 6 7 8 9 10 Roses 0 5 18 78 108 136 156 143 123 89 a) What is the average product of fertilizer when tons are used? b) What is the marginal product...
A firm uses two inputs, capital K and labor L, to produce output Q that can...
A firm uses two inputs, capital K and labor L, to produce output Q that can be sold at a price of $10. The production function is given by Q = F(K, L) = K1/2L1/2 In the short run, capital is fixed at 4 units and the wage rate is $5, 1. What type of production function is F(K, L) = K1/2L1/2 ? 2. Determine the marginal product of labor MPL as a function of labor L. 3. Determine the...
A firm uses two inputs x1 and x2 to produce output y. The production function is...
A firm uses two inputs x1 and x2 to produce output y. The production function is f(x1, x2) = (x13/2+ x2)1/2. The price of input 1 is 1 and the price of input 2 is 2. The price of output is 10. (a) Calculate Marginal Products for each input. Are they increasing or decreasing? Calculate Marginal Rate of Technical Substitution. Is it increasing or diminishing? (b) Draw two or more isoquants. Does this production function exhibit increasing, decreasing or constant...
1) A firm uses two inputs in production: capital and labor. In the short run, the...
1) 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) a) Average fixed cost b) Marginal cost c) Average total cost d) Average variable cost 2) If the cost of hiring workers increases, which of...
A firm uses capital and labor to produce output according to the production ? = 4√??...
A firm uses capital and labor to produce output according to the production ? = 4√?? (a) Find the marginal product of labor (MPL) and marginal product of capital (MPK). (b) If the wage w=$1/labor-hr. and the rental rate of capital r=$4/machine-hr., what is the least expensive way to produce 16 units of output? (c) What is the minimum cost of producing 16 units? (d) Show that for any level of output, q, the minimum cost of producing q is...
Consider a firm that used only two inputs, capital (K) and labor (L), to produce output....
Consider a firm that used only two inputs, capital (K) and labor (L), to produce output. The production function is given by: Q = 60L^(2/3)K^(1/3) . a.Find the returns to scale of this production function. b. Derive the Marginal Rate of Technical Substitutions (MRTS) between capital and labor. Does the law of diminishing MRTS hold? Why? Derive the equation for a sample isoquant (Q=120) and draw the isoquant. Be sure to label as many points as you can. c. Compute...
a. A firm uses only two inputs: capital (K) and labor (L).Currently, the firm’s choice of...
a. A firm uses only two inputs: capital (K) and labor (L).Currently, the firm’s choice of capital (K) and labor (L) are such that marginal product of capital is 80 and the marginal product of labor is 10. If one put Labor on the x-axis, derive the slope of the firm’s isoquant given the information above (include the formula you use to do this). b. The price of capital (Pk) is $40 and the price of labor (PL) is $20....
1. Consider a firm with the following production function: Q= 60 L^2 K^1/2 -4L^3 The firm...
1. Consider a firm with the following production function: Q= 60 L^2 K^1/2 -4L^3 The firm is operating in the short run with a fixed capital stock of K=4 Use this to answer the following questions: 2. Suppose the firm in the previous question is able to increase its capital to K ¯ = 9.   After what quantity of labor does diminishing marginal returns now occur? What is the maximum output the firm can now produce? After what number of...
Problem 3 [24 marks] A competitive firm uses two inputs, capital (?) and labour (?), to...
Problem 3 [24 marks] A competitive firm uses two inputs, capital (?) and labour (?), to produce one output, (?). The price of capital, ??, is $1 per unit and the price of labor, ??, is $1 per unit. The firm operates in competitive markets for outputs and inputs, so takes the prices as given. The production function is ?(?,?) = 3?0.25?0.25. The maximum amount of output produced for a given amount of inputs is ? = ?(?,?) units. a)...
1- - As a firm expands by adding more of the variable input to fixed inputs,...
1- - As a firm expands by adding more of the variable input to fixed inputs, it experiences: a) constant returns, diminishing returns, increasing returns b) diminishing returns, constant returns, increasing returns c) increasing returns, constant returns, diminishing returns d) diminishing returns, increasing returns, constant returns 2- The Production Function is: a) a curve concave to the origin b) an upside down parabola c) A straight line sloping upward d) An "S" curve 3- The production function shows : a)...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT