Note: In order to get full marks you need to explain and show all your
1. Explain following terms: (14 points)
Production function, Marginal product, Isoquant curve,
TRS, Returns to scale, Isoprofit line,
2. For each of following production functions comment on the ability to
substitute capital for labor. Note that Q, K, and L denote output, capital, and labor
respectively. (6 points)
Q ? K ? L
0.5 0.5 Q ? K L
Q ? min?K, L?
3. Justify whether the following statement is true or false. “If the production
1 2 1
y ? f (x , x ) ? x x
, then it exhibits constant returns to scale.” (5
4. Justify whether the following statement is true or false. “If the value of the
marginal product of labor exceeds the wage rate, then a competitive, profit
maximizing firm would want to hire less labor.” (5 points)
Problem 1: (10 points)
A profit-maximizing competitive firm uses just one input, x, to produce output y.
Its production function is:
y ? 8x
The price of output is 40$ each unit and the factor price is 8$ each unit.
a. Find profit-maximizing output and the amount of the factor that the firm
demands. (5 points)
b. Find also the maximum profits. (Hint: the marginal product of the factor
.) (5 points)
Problem 2: (10 points)
Weeding a vegetable patch only requires labour as an input. The output of such
an activity is the number of square meters weeded per day, defined as Y. The
relationship between Y and the amount of labour L is:
Y = 20L1/2
a. Draw this relationship on a graph and label it. (5 points)
b. Is the marginal product of labour always positive? Does this relationship
obey the “law” of diminishing marginal returns? (5 points)
Problem 3: (26 points)
A farmer uses two inputs (labour:L, and Fertilizer:F) to produce his only output
(corn: C). His production function is :
1/2 1/2 C?f(L,F) ? 2L F .
a- Derive the expressions of marginal product of labour
product of fertilizer
. (4 points)
b- Use your answers in (a) to check if the decreasing marginal return law is
verified. (4 points)
be the wage per hour and
the price per one kg of fertilizer.
What is the long run cost-minimization condition for this farmer given his
technology of production described above? (4 points)
d- What would be the ratio of labour to fertilizer knowing that
W ? $4
? (2 points)
e- What are the optimal amounts of labour and fertilizer that this farmer
should use to produce 1kg of corn? (3 points)
f- What would be the cost of producing 1kg of corn? (2 points)
g- In general, given his production function, if the farmer doubles the
amount of the inputs by how much would the output be multiplied? What
does this tell you about the returns to scale? (3 points)
h- Is the answer in (g) in contradiction with the answers found in (b)?
Clearly explain. (4 points)
PLACE THIS ORDER OR A SIMILAR ORDER WITH US TODAY AND GET A GOOD DISCOUNT 🙂
Delivering a high-quality product at a reasonable price is not enough anymore.
That’s why we have developed 5 beneficial guarantees that will make your experience with our service enjoyable, easy, and safe.
You have to be 100% sure of the quality of your product to give a money-back guarantee. This describes us perfectly. Make sure that this guarantee is totally transparent.Read more
Each paper is composed from scratch, according to your instructions. It is then checked by our plagiarism-detection software. There is no gap where plagiarism could squeeze in.Read more
Thanks to our free revisions, there is no way for you to be unsatisfied. We will work on your paper until you are completely happy with the result.Read more
Your email is safe, as we store it according to international data protection rules. Your bank details are secure, as we use only reliable payment systems.Read more
By sending us your money, you buy the service we provide. Check out our terms and conditions if you prefer business talks to be laid out in official language.Read more