ARE 100
University of California, Davis
Department of Agricultural and Resource Economics
ARE 100B
Dr. Larson
Winter 2010
Problem Set 3
Answers
1. Intel is a monopolist manufacturing computer chips with a competitive fringe of firms that act as price takers of the price Intel sets. The market willingness to pay for the P80 chip is given by= 400 − Q, with p in dollars p F per chip and Q in thousands of chips per month. The fringe marginal cost curve is MC= 40 + .5Q F (with Q F
and MC F also in thousands of chips and dollars per chip, respectively), and Intel's marginal cost of producing chips is constant at $50 per chip. Intel is planning its strategy to set the P80 chip price.
(a) Determine the residual demand Intel faces after accounting for the quantity supplied by the competitive fringe for any level of price.
The residual demand that Intel can work with is the difference between total quantity demanded and the quantity supplied by the fringe at any given price. Total demand is= 400 − p, and fringe supply is Q f 2( p − 40),
=
Q for prices above 40. Thus the residual demand is
Q r =Q − Q f =(400 − p ) − 2( p − 40) =480 − 3 p.
(b) How many P80 chips will Intel supply per month?
The inverse demand facing Intel is p r = − (1/ 3) ⋅ Q r , so Intel's marginal revenue is
160
MR r = − (2 / 3) ⋅ Q r . Setting this equal to Intel's MC,
160
MR r = 160 − (2 / 3) ⋅ Q r = 50 = MC r ,
Q r =− 50) /(2 / 3) =
(160
165.
Intel will supply 165 thousand chips per month.
(c) What is the resulting world P80 chip price?
The resulting world price is set from the Intel residual inverse demand: p = 160 − (1/ 3) ⋅165 = $105 per chip.
(d) How many P80 chips are supplied by the competitive fringe?
The competitive fringe takes the price of oil as given, so from its supply function
Q f =⋅ (105 − 40) = thousand chips per month.
2
130
2. You and another firm are a duopoly supplying the market for bread in Davis. The inverse aggregate demand you both face
Department of Agricultural and Resource Economics
ARE 100B
Dr. Larson
Winter 2010
Problem Set 3
Answers
1. Intel is a monopolist manufacturing computer chips with a competitive fringe of firms that act as price takers of the price Intel sets. The market willingness to pay for the P80 chip is given by= 400 − Q, with p in dollars p F per chip and Q in thousands of chips per month. The fringe marginal cost curve is MC= 40 + .5Q F (with Q F
and MC F also in thousands of chips and dollars per chip, respectively), and Intel's marginal cost of producing chips is constant at $50 per chip. Intel is planning its strategy to set the P80 chip price.
(a) Determine the residual demand Intel faces after accounting for the quantity supplied by the competitive fringe for any level of price.
The residual demand that Intel can work with is the difference between total quantity demanded and the quantity supplied by the fringe at any given price. Total demand is= 400 − p, and fringe supply is Q f 2( p − 40),
=
Q for prices above 40. Thus the residual demand is
Q r =Q − Q f =(400 − p ) − 2( p − 40) =480 − 3 p.
(b) How many P80 chips will Intel supply per month?
The inverse demand facing Intel is p r = − (1/ 3) ⋅ Q r , so Intel's marginal revenue is
160
MR r = − (2 / 3) ⋅ Q r . Setting this equal to Intel's MC,
160
MR r = 160 − (2 / 3) ⋅ Q r = 50 = MC r ,
Q r =− 50) /(2 / 3) =
(160
165.
Intel will supply 165 thousand chips per month.
(c) What is the resulting world P80 chip price?
The resulting world price is set from the Intel residual inverse demand: p = 160 − (1/ 3) ⋅165 = $105 per chip.
(d) How many P80 chips are supplied by the competitive fringe?
The competitive fringe takes the price of oil as given, so from its supply function
Q f =⋅ (105 − 40) = thousand chips per month.
2
130
2. You and another firm are a duopoly supplying the market for bread in Davis. The inverse aggregate demand you both face