isi 2009

[seema]

6. Consider an industry with 3 firms, each having marginal cost equal to 0. The
inverse demand curve facing this industry is p = 120 − q, where q is aggregate
output.

• (iii) Firms 2 and 3 decide to merge and form a single firm with marginal
cost still equal to 0. What output do the two firms produce in equilibrium?
Is firm 1 better off as a result? Are firms 2 and 3 better off post-merger?
Would it be better for all the firms to form a cartel instead? Explain in
each case.

When all three firms merge, how are they better off ?

[seema]

7. Suppose the economy’s production function is given by
Yt = 0.5(Kt)^1/2 * (Nt)^1/2      (1)
Yt denotes output, Kt denotes the aggregate capital stock in the economy, and
N denotes the number of workers (which is fixed). The evolution of the capital
stock is given by,
Kt+1 = sYt + (1 −dep )Kt    (2)
where the savings rate of the economy is denoted by, s

• (iv) Is there a savings rate that is optimal, i.e., maximizes steady state
consumption per worker ? If so, derive an expression for the optimal
savings rate.

i am getting optimal saving rate as 0.5. is it correct?

[s]

hey i got ...
capital labour ratio=k=16
rate of growth of output=.05
rate of growth of savings=.05
wage rate=2

[deepak]

For Q 6)
When the firms stay separate, Profit in each case = 900
When firms 2 and 3 merge, profit(1) = 1600 and profit of the merged firm = 1600 < 2*900(when they stayed separate). Hence firm 1 is better off when the other 2 merge. Firms 2 and 3 are worse off than earlier.
When the firms behave as a cartel, collective profit is 3600. Since they are symmetric, each firm has a profit of 1200. Hence all of them are better off when compared with when they existed as individual entities.

For Q 7)
y* = s/2del
c* = (1-s)y = (1-s)*s/2del
c* is max at s = 0.5 so yes. That's what i get too.

[aastha]

@ deepak :


for ques 6 : i got the same ans as yours . .

for ques 7 : could u pls explain how did u arrive at these ans ??

thanks in advance

[deepak]

Change in capital per capita dk = sy - del k
At steady state, the change in capital is 0 ie LHS = 0
This gives sy = del k. Given y = k^.5 Hence we can calculate steady state output to be s/4del
Now consumption is
C = y - ys = y(1-s)
and y = s/4del
substitute that here and maximize c by taking first order and you will get s = 0.5

Hope this helps

[Smith]

How did you calculate wage rate???