Math Solutions

[Solution] [Profit maximizing input demand] Consider a competitive firm with the following profit function \Pi =R-C=PQ-wL-rK where P = Price of the output

Question: [Profit maximizing input demand]

Consider a competitive firm with the following profit function

\[\Pi =R-C=PQ-wL-rK\]

where

P = Price of the output

Q = Output

L = Labor input

K = Capital input

w = wage rate for labor input

r = rental rate for capital input

and

\[Q\left( K,L \right)=16{{K}^{\frac{1}{4}}}{{L}^{\frac{1}{4}}}\]
  1. Find the input quantities K* and L* that satisfy the first order conditions for the profit maximization. Assume the parameter values P = 4, w = 1, and r = 1.
  2. Compute the profit maximizing output Q*.
  3. Compute the maximum profit \(\Pi *\).
  4. If the wage rate w changes to w = 2, determine the new L**.
  5. If the rental rate r changes to r = 2, determine the new L**.
  6. If the output price P changes to P = 16, determine the new L**. Hint: All other parameters remain as in the original case in last three parts.
  7. Also compute the profit maximizing output Q** and the maximum profit in each case II** in each of the last three parts, i.e., (d)-(f).

Price: $2.99
Solution: The downloadable solution consists of 4 pages
Deliverable: Word Document


∴ Other downloads you may be interested in ∴

log in to your account

Forgot password?
Don't have a membership account?
REGISTER

reset password

Back to
log in

sign up

Back to
log in