产业组织理论-考题--英文

1.Because both pencils and erasers in a ratio of 2:3
Get the two goods equal weight ，that is ：
6.04.021==λλ
Then ，that is ：
①Ray average costs:
q
q q q
q q q q
q q C q q q C q RAC 2
22132.016.032006.02.0)4.0(24.01.03200)6.0,4.0(),()(++=⨯+⨯+⨯+===λλ ②The production minimizes the ray average costs,need s equal to 1:
1
01.004.002.001.020016.064.032.016.032002
.06.0)4.041.0(4.032.016.032002
.0)41.0(32.016.03200)
(22
22
2
2112
2
211=+++=+++=⨯+⨯+⨯++=⨯++⨯++=∂∂+∂∂=q
q q q q
q q q q q q q q q q q q q q C q q C q q C s
We get 100=q ,so 606.0404.021====q q q q .
③when only produced pencils:
02=q
2
11121.03200)0,(q q q C ++=
11
121.0)(q q q AC ++= When )(1q AC is minimized ，the firm would minimum efficient scale
We can get 401=q 。

④This is the same to ，we can get 02=q
2.we have known the market demand curve is p Q -=100
①The market price elasticity of demand ：
100
)1(-=⋅-=⋅∆∆=∆∆=p p Q p Q p p Q p
p Q Q
E p ②The supply curve of the whole market ： p q Q s 5050==
At the competitive equilibrium ：51
100==p Q Q s Residual demand curve p p p p S Q p D o r 5010049100)()(-=--=-=
We use MATLAB ，
x=linspace(0,2);
y=100-50*x;
plot(x,y,'r')
Can get the chart as following ：
The residual demand elasticity facing one firm )1(--=n n o i ηεε
100-=⋅∆∆=∆=p p
Q p
p Q
p
p Q
ε
15050-=⨯-=⋅=p p
q p
dp dD r
o η
48)150)(1(50100=---⨯-=p p
i ε
3.the demand curve is p p Q =)(
①The elasticity of demand is ε=⋅=Q p
dp dQ
E p
②when the profit-maximizing MC MR = 0=-+=-+MC Q dQ dp
p dQ dC
Q dQ dp p
2=p
4.When in a cartel ，those firms make the total profit max
Q Q Q Q
Q Q TC pQ t 961112
)11114(11)100(22
+-=+⋅⋅--=-=π ①0=dQ d π
44=Q
5644100100=-=-=Q p
4=q
19211==t
ππ
②when the other firms maintain the cartel price ，56=p
For the cheated firm ，24)(q q pq q c pq o --=-=π
If it keeps its price at 56 ，its 26=q 676=o π
5.if the firms initially collude ：
①in the first period ，assume Firm1 by cheating on the agreement and competing instead ，it
will get $25 extra ;
So ，in the second period ，Firm2 will retaliate by refusing to collude in this period ，for Firm1 ，it will get $5 less;
…………
Because 2555=⨯
So ，for five periods would such retaliation have to last to deter cheating if the interest rate is 0%。

②Yes.Assume the rate is r ，if the rate were positive ，the present value of the $5 getting from each period will be less than $5 ，this minimum retaliation period would be longer 。

Because high interest rate will discount future profits.
③If the rate is 10%：
251
.151.151.152=+++n
8=n
④Assume the rate is r ，in order to keep that there is no retaliation ever deters cheating ： %2025)1(5)1(5152≥⇒≤++++++∞+r r r r。