{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

midtrmsol_a - 1 Maxcfw_qi NPV = Maxcfw_qi L = F.O.C L =...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
1. ( 29 0,1 i for subject to ) ( ) ( i r) (1 1 NPV 0 1 0 } { = = - + = = S q q C q B Max i i i i q i ( 29 - + - = = + 1 0 0 r) (1 1 } , { S ) ( ) ( L i i i i i q q q C q B Max i l l F.O.C 0 0 )) ( ' ) ( ' ( 1 1 0 ) ( ' ) ( ' 1 0 0 1 1 1 0 0 0 = - - = = - - + = = - - = q q S L q C q B r q L q C q B q L l l l (1) From which we get the following important inter-temporal equilibrium conditions 0 1 0 1 1 0 0 ) ( ' ) ( ' 1 1 ) ( ' ) ( ' S q q q C q B r q C q B = + - + = - (2) Perfect Competition In perfect competition 1 , 0 for ) ( ' = = i q B P i i Since we know that 1 , 0 for 5 . 1000 = - = i q P i i , 1 , 0 for 400 ) ( ' = = i q C i , and % 10 = r , then (2) becomes 1000 ) 5 . 0 600 ( 1 . 1 1 5 . 0 600 1 0 1 0 = + - = - q q q q (3) The solution to the above simultaneous system of equation is 66 . 466 * 33 . 533 * 1 0 = = q q To find the market price in each period just substitute q into the demand equations. 66 . 766 ) 66 . 466 ( 5 . 1000 *) ( 5 . 0 1000 33 . 733 ) 33 . 533 ( 5 . 1000 *) ( 5 . 0 1000 1 1 0 0 = - = - = = - = - = q P q P To find l use the first equation of the F.O.C system (1) 33 . 333 400 33 . 733 ) ' *) ( ' *) ( ' *) ( ' 0 0 0 0 0 0 = - = - = - = - = q C p q C P q C q B l
Background image of page 1

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

View Full Document Right Arrow Icon
Monopolist Under the monopolist the marginal benefit is not equal to the price. Competitive Market: B(q) = pq (price is given) B’(q) = p Monopolist: B(q) =p(q)q (price is affected by monopolist’s output) B’(q) = p(q) + p’(q)q Therefore, in this case we have the following: % 10 2 , 1 for 400 ) ( ' 2 , 1 for 1000 ) ( ' = = = = - = r i q C i q q B i i i So (2) becomes 1000 ) 600 ( 1 . 1 1 600 1 0 1 0 = + - = - q q q q (4) The solution to the above simultaneous system of equation is 23 . 495 76 . 504 1 0 = = m m q q To find the market price in each period just substitute q into the demand equations. 38 . 752 ) 23 . 495 ( 5 . 1000 ) ( 5 . 0 1000 62 . 747 ) 76 . 504 ( 5 . 1000 ) ( 5 . 0 1000 1 1 0 0 = - = - = = - = - = m m q P q P To find m l use the first equation of the F.O.C system (1) 23 . 95 400 76 . 504 1000 ) ( ' 1000 *) ( ' *) ( ' 0 0 0 0 = - - = - - = - = m m m q C q q C q B l Open Access
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}