DSE 2004 Q.24 and Q.25

[Do bats eat cats?]

Link to paper

I have no idea how to do these questions. I can't quite understand how the economy described in situation VII is even relevant. I'm probably missing something trivial, so any help or even a nudge in the right direction will be appreciated.

Thanks!

[maahi]

hi
 i have same doubts
 were u able to do q 20 - 23 ?? if yes , please help me .

[Do bats eat cats?]

My solutions are messy and could be completely incorrect, so proceed with caution.

Q. 20
Markets will clear when D(w) = S(w) or at w = 1/2.
The corresponding employment level is equal to 1/2.
So, the aggregate supply is f(1/2).

Q. 21
The nominal wage rate W minimises |D(W/P) — S(W/P)|.
Or, it minimises |(1-(W/P)) - (W/P)| = |1 -(2W/P)|.
The minimum value of this expression is 0, which is achieved when 2W/P = 1 or W = P/2.
However, we are given the constraint W ≥ W0.
So, if P/2 ≥ W0, the minimum value is obtained at W = P/2.
If P/2 < W0, the constrained minimum value is obtained at W = W0.
Note that we are choosing max {W0, P/2}, which is the required answer.

Q. 22
The nominal wage is given by max {W0, P/2}.
If W0 ≥ P/2, then W = W0 and w = W0/P.
Labour demand is given by D(w) = 1 - w. So, employment level is 1 - W0/P.
If P/2 ≥ W0, then W = P/2, and w= 1/2.
Hence, labour demand, and employment level is also 1/2.
In this case, we are choosing from min {1/2, 1 - W0/P}.

Q. 23
Now, 1/2 < 1- W0/P.
From the previous answer, we can deduce that the employment level is 1/2.
So, the aggregate supply is f(1/2).

In case you're wondering, yes, I'm working on my verbosity.

[maahi]

Do bats eat cats? wrote

My solutions are messy and could be completely incorrect, so proceed with caution.

Q. 20
Markets will clear when D(w) = S(w) or at w = 1/2.
The corresponding employment level is equal to 1/2.
So, the aggregate supply is f(1/2).

thats real wage w . why are u taking it equal to emp level??


Q. 21
The nominal wage rate W minimises |D(W/P) — S(W/P)|.
Or, it minimises |(1-(W/P)) - (W/P)| = |1 -(2W/P)|.
The minimum value of this expression is 0, which is achieved when 2W/P = 1 or W = P/2.
However, we are given the constraint W ≥ W0.
So, if P/2 ≥ W0, the minimum value is obtained at W = P/2. isn't d min value WO

If P/2 < W0, the constrained minimum value is obtained at W = W0. isn't min at p/2
Note that we are choosing max {W0, P/2}, which is the required answer. why are we choosing max fn .

Q. 22
The nominal wage is given by max {W0, P/2}.
If W0 ≥ P/2, then W = W0 and w = W0/P.
Labour demand is given by D(w) = 1 - w. So, employment level is 1 - W0/P.
If P/2 ≥ W0, then W = P/2, and w= 1/2.
Hence, labour demand, and employment level is also 1/2.
In this case, we are choosing from min {1/2, 1 - W0/P}.

Q. 23
Now, 1/2 < 1- W0/P.
From the previous answer, we can deduce that the employment level is 1/2.
So, the aggregate supply is f(1/2).

In case you're wondering, yes, I'm working on my verbosity.

[Do bats eat cats?]

Because at w = 1/2, demand and supply of labour is 1/2?
D(w) = 1 - w and S(w) = w. I substituted the market clearing wage in the equations.

I hope I'm not confusing you further

[maahi]

ok ya sorry ...

[Do bats eat cats?]

There's a much better explanation for 21 here.