Ceteris paribus, the more these two firms to produce, the lower the market price will be.
- In this case, the equilibrium price may be decided by firm1, and outputs will be higher and higher, price will be lower and lower, profit will shrink because the supply quantity will largely exceed the quantity demanded by the consumers.
- If firm 2 moves first that makes firm 2 the market leader.
For any Q, firm 1 will choose q1 on its best response function. Thus firm 2 chooses q2 to maximize its profit.
Firm 1: Quantity=q1, Unit cost=c1,
Firm 2: Quantity=q2, Unit cost=c2,
Industry Demand Curve p=a-Q (a>0)
Q= q1+ q2
-
c2 > c1>0
Analyse the Stackelberg equilibrium where Firm 2 is the leader:
π1=pq1-Mc1 q1=(a-Q) q1- Mc1 q1=(a- q1- q2) q1- Mc1q1 =(a- Mc1) q1- q12 - q1 q2
δπ1/δq1=0 => a-Mc1- 2q1- q2=0
=>q1=(a-Mc1- q2)/2 q1*=(a-Mc1- q2)/2 (1) Reaction Function for firm 1
by symmetry q2*=(a-Mc2- q1)/2 (2)
substitute (2) in (1)
q1=(a-2Mc1+Mc2)/3 => q1*=(a-2Mc1+Mc2)/3
q2=(a-2Mc2+Mc1)/3 => q2*=(a-2Mc2+Mc1)/3
P=a-Q=a- q1-q2=a-(a-2Mc1+Mc2)/3-(a-2Mc2+Mc1)/3 = (a+Mc1+Mc2)/3
π1=[a- q1- (a-2Mc2+Mc1)/3]q1 - Mc1 q1
π2=pq2-Mc2 q2
=(a+Mc2+Mc1)/3 *(a-2Mc2+Mc1)/3-Mc2*(a-2Mc2+Mc1)/3
=2/3(a+Mc2+Mc1)q2-q22
δπ2/δq2=0 =>2/3(a+Mc2+Mc1)-2q2 =0
q2=3(a+Mc1-Mc2)
q1=Mc2-a-2Mc1
=> p=-a-Mc1+2Mc2
π1=( Mc2-a-2Mc1)2 –Mc1 (Mc2-a-2Mc1) = (Mc2-a-2Mc1)( Mc2-a-3Mc1)
π2 = (Mc1-a-2Mc2)( Mc1-a-3Mc2)
π2< π1 so, Firm 1 (follower is making more profits)
Question 2:
Contract Curve: In an exchange economy, all efficient allocations of the existing goods lie along a (multidimensional) contract curve. Points off that curve are necessarily inefficient, since individuals can be made unambiguously better off by moving to the curve. Along the contract curve, however, individuals’ preferences are rivals in the sense that one individual’s situation may be improved only if someone else is made worse off. The set of all the efficient allocations in an Edgeworth Box diagram is called contract curve.
Suppose that simple two good X and Y, and two consumer a and b. Along Oa, Ob, the MRS for consumer a is equal to that for consumer b. The line Oa, Ob is the contract curve in figure 1.
Any point for which the MRS for consumer a is unequal to that for consumer b presents such an opportunity. When the Marginal rates of substitution of consumer a and b are equal, however such mutually beneficial trades are not available. Any points lies on the line Oa, Ob indicate tangencies of these individuals’ indifference curves and movement away from such points must take at least one of the consumer worse off. Points off the contract curve represent the exhaustion of all such trading opportunities.
When the two consumers a and b have identical preferences, which means there is no competition at all. whatever utility function they choose, the output remain the same so in this case the contract curve is a straight line as the following figure 2.
Bibliography:
Microeconomics Theory (MAS-COLELL WHINSTON AND GREEN)
Microeconomics (H GRAVELLE & R REES) SECOND EDITION
Microeconomics Theory (NICHOLSON, 4th ED.)