Ec146_soln_midterm

# Ec146_soln_midterm - EC 146 Industrial Organization...

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

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: EC 146: Industrial Organization Solutions to the Midterm Exam Department of Economics Brown University October 26, 2007 1. (a) Let’s solve the problem of Firm i . I takes the output choices of the other firms as given and solves Max { q i } π i = h 100- ( q i + q- i ) i q i , where q- i = ∑ j 6 = i q j . The first order condition is 100- 2 q i- q- i = 0 . Hence, the best response function of Firm i is q BR i ( q 1 ,...,q i- 1 ,q i +1 ,...,q n ) = 100- q- i 2 . (1) Notice that the best response functions will be symmetrical, so the solution of this system of n equations and n unknowns is such that in equilibrium, each firm produces the same quantity. That is, q 1 = q 2 = ... = q n = q , which implies that q- i = ( n- 1) q . Equation (1) thus becomes q = 100- ( n- 1) q 2 . In the Cournot-Nash equilibrium, therefore, each firm produces q 1 = q 2 = ... = q n = 100 n + 1 . Total output and price are in equilibrium Q = 100 n n + 1 P = 100 n + 1 . The profit that each firm obtain in equilibrium is π i = ‡ 100 n + 1 · 2 ....
View Full Document

{[ snackBarMessage ]}

### Page1 / 4

Ec146_soln_midterm - EC 146 Industrial Organization...

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

View Full Document
Ask a homework question - tutors are online