Doubts in "DSE Type Test" (Mock by Amit sir)

[Ridhika]

Can someone please explain the following questions in this paper?

31. A competitive industry faces the demand x = 865 – 5p
Where x is the industry output and p is the price of the product. There are n firms having identical
cost conditions Ci
 = 144 + 5xi +4xi^2 where xi
 is the output of firm i and Ci is its total cost.
There is free entry and large number of potential entrants.
Equilibrium output and price of the industry is
a) (x, p) = (690, 35)
b) (x, p) = (600, 53)
c) (x, p) = (515, 70)
d) None of the above
 
32. In the preceding question, number of firms who will enter the industry is
a) 115
b) 100
c) 90
d) None of the above

I cant solve 31 without knowing the number of firms..

[hs]

equate ac=mc get x
put x in mc get x
now mc =p =53 so option b correct

now x was 6 ..total out put 600
for 1 firm 600/6=100

[Ridhika]

Thanks a lot Himanshu!

[hbk]

31 option b
32 option c
equate mc and ac get value of x
substitute in price eqn and get p
then two find no of firms nq=Q
where Q is agg and q is of single firm..

[hs]

can sum 1 help me with q6 with figure
6. A consumer has a utility function u(x, y) = max{2x + y, x + 3y}. He consumes (1, 0) in
equilibrium. Then which of the following must be true?
a) px <= py
b) px  <=(3/2)py
c) px  <=(2/3)py
d) px < py