d TC amount of seed money and is deciding to allocate it pital in the least cost way. The production function of nas Q = 25LKb which acts as the production target parameter] s of marginal product of labor and capital and write the minimization problem prium conditional labor and capital demand functions. You an or the first order conditions & directly use the tangency put target to solve for these. litional factor demand functions (for both factors of ively sloping in input prices. cost function and find the expressions of Average Cost AC and Marginal Cost on one graph. Comment on how with quantity produced.
d TC amount of seed money and is deciding to allocate it pital in the least cost way. The production function of nas Q = 25LKb which acts as the production target parameter] s of marginal product of labor and capital and write the minimization problem prium conditional labor and capital demand functions. You an or the first order conditions & directly use the tangency put target to solve for these. litional factor demand functions (for both factors of ively sloping in input prices. cost function and find the expressions of Average Cost AC and Marginal Cost on one graph. Comment on how with quantity produced.
Chapter11: The Firm: Production And Costs
Section: Chapter Questions
Problem 15P
Related questions
Question
![Suppose a firm hires from the competitive labor and capital market to make
strawberries. The per unit price of labor is $w and the per unit price of capital is
$r. The firm has raised TC amount of seed money and is deciding to allocate it
on hiring labor and capital in the least cost way. The production function of
strawberries is written as Q = 25LKb which acts as the production target
[0<b<1 is an unknown parameter]
a) Find the expressions of marginal product of labor and capital and write the
statement of the cost minimization problem
b) Solve for the equilibrium conditional labor and capital demand functions. You
can omit the Lagrangian or the first order conditions & directly use the tangency
condition and the output target to solve for these.
c) Prove that the conditional factor demand functions (for both factors of
production) are negatively sloping in input prices.
d) Find the minimized cost function and find the expressions of Average Cost
and Marginal Cost
e) Draw the graphs of AC and Marginal Cost on one graph. Comment on how
these curves behave with quantity produced.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2ee27961-2d98-4069-bd8e-4c3d99346202%2F5eab398e-5c09-447c-aacb-126c33068575%2Fuarf82dp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Suppose a firm hires from the competitive labor and capital market to make
strawberries. The per unit price of labor is $w and the per unit price of capital is
$r. The firm has raised TC amount of seed money and is deciding to allocate it
on hiring labor and capital in the least cost way. The production function of
strawberries is written as Q = 25LKb which acts as the production target
[0<b<1 is an unknown parameter]
a) Find the expressions of marginal product of labor and capital and write the
statement of the cost minimization problem
b) Solve for the equilibrium conditional labor and capital demand functions. You
can omit the Lagrangian or the first order conditions & directly use the tangency
condition and the output target to solve for these.
c) Prove that the conditional factor demand functions (for both factors of
production) are negatively sloping in input prices.
d) Find the minimized cost function and find the expressions of Average Cost
and Marginal Cost
e) Draw the graphs of AC and Marginal Cost on one graph. Comment on how
these curves behave with quantity produced.
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