{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

profitmaxspring06

profitmaxspring06 - Profit Maximization Example Suppose f(L...

This preview shows pages 1–2. Sign up to view the full content.

Pro fi t Maximization - Example Suppose f ( L, K ) = 4 L 1 4 K 1 2 .Let prices be p = 1 , w L = 2 and w K = 1 . Method 1 (direct long run pro fi t maximization) max L,K ³ 4 L 1 4 K 1 2 w L L w K K ´ s.t. L 0 , K 0 In an interior solution, FOC: 4 × 1 4 L 3 4 K 1 2 = 2 4 × 1 2 L 1 4 K 1 2 = 1 Dividing one condition by the other we fi nd 1 2 K L = 2 K = 4 L. Substitute into the fi rst condition and solve for L: 4 × 1 4 L 3 4 (4 L ) 1 2 = 2 L = 1 K = 4 L = 4 y = 4 L 1 4 K 1 2 = 8 . Pro fi t equals π = AL 1 4 K 1 2 w L L w K K = 8 2 × 1 4 = 2 . Method 2 Step 1- fi nd cost function. Step 2 fond pro fi t maximizing output. Step 1: The long run cost is the solution to: min L,K (2 L + K ) s.t. L 0 , K 0 and 4 L 1 4 K 1 2 = y. When y > 0 the solution must be interior. If one of the inputs is zero the quantity produced is zero. In an interior solution we know that TRS = w L w K and f ( L, K ) = y K 2 L = 2 4 L 1 4 K 1 2 = y. 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
We solve the system. The fi rst equation implies that
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 2

profitmaxspring06 - Profit Maximization Example Suppose f(L...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online