Doubts

[Rautparul]

Hi..  I am stuck with this question. Can anybody explain what is happening?

Consider a two-person two-good exchange economy, where
agents are denoted by A, B and goods are denoted by X, Y . A Pareto optimal
allocation of this economy may not remain Pareto optimal if

(a) Everything else remaining the same, Agent A transfers a part of her
endowment to Agent B
(b) Everything else remaining the same, Agent A gets additional endowment
(c) Everything else remaining the same, Agent A's utility function is monotonically transformed
(d) All of the above

Also, what is the idea behind Pareto optimal and equilibrium price? How are they different to each other?

[Amit Goyal]

To know the what Pareto efficiency and competitive equilibrium means, watch the videos in this playlist:
https://www.youtube.com/playlist?list=PLUJGfL_499TKsujAH6aeObLCw5VvSjzAx

It will take you less than a couple of hours to watch all of them in the list. It will help you in answering questions like these.

[Amit Goyal]

Answer to this problem is
(b) Everything else remaining the same, Agent A gets additional endowment

This changes the dimension of Edgeworth box, so initial allocation may no longer be efficient.

[Rautparul]

Sure.. Thank You Sir!!

[Rautparul]

A firm has the production function f(x1, x2) = x1^0.40 x2^0.20
The isoquant on which output is
40^(2/10) has the equation:

(a) x2 = 40x1^-2

(b) x2 = 40x1^5

(c) x1/x2 = 2

(D) x2 = 40x1^-0.2

(e)x1 = 0.20x2^-0.80

[Abhitesh]

x1^.4 * x2^.2 = 40^.2
=> x1^(2*.2) * x2^.2 = 40^.2
=> (x1^2 * x2) ^.2 = 40^.2
=> x1^2 * x2 = 40
=> x2 = 40*x1^-.2

[Rautparul]

But the answer is D option

On 24-Jan-2017 9:26 PM, "Abhitesh [via Discussion forum]" <[hidden email]> wrote:

x1^.4 * x2^.2 = 40^.2
=> x1^(2*.2) * x2^.2 = 40^.2
=> (x1^2 * x2) ^.2 = 40^.2
=> x1^2 * x2 = 40
=> x2 = 40*x1^-.2

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[Rautparul]

This is a very lame doubt. But I am stuck with basics:

True/False
A competitive, cost-minimizing rm has the production function f(x; y) = x + 2y and uses
positive amounts of both inputs. If the price of x doubles and the price of y triples, then the cost
of production will more than double

Apparently, Answer is False.

I am not getting how to derive cost function from production function. Is there a direct way?

[Rautparul]

A competitive firm uses two inputs, x and y. Total output is the square root of x times
the square root of y. The price of x is 17 and the price of y is 11. The company minimizes its costs
per unit of output and spends $517 on x. How much does it spend on y?
(a) 766
(b) 480
(c) 655
(d) 517
(e) None of the above.

The answer is D. But how?

[Rautparul]

Hello folks,  can anyone help out with this one?

Douelberry juice is a mild intoxicant, prized for facilitating conversation among university
administrators, but not otherwise valued. The berry does not travel well, so it must be squeezed on
the farm where it is grown. Baskets of berries are produced using ounces of seeds, S; and hours la-
bor, L; according to a production function B = S1/2L1/2. Gallons of Juice, J; are made from baskets
of berries and hours of labor according to the production function J = min(B;L). If seeds cost 9
per ounce and labor costs 1 per hour, what is the cost of producing each gallon of douelberry juice?
(a) 14
(b) 6
(c) 3
(d) 7
(e) Since there are not constant returns to scale, the cost per gallon depends on the number of gallons
produced.

The answer is d but I am getting c.

I tried solving.. attaching file.. can anybody point out where is it wrong?

[Abhitesh]

Since positive amount of both inputs are used. So py=2px.
If py>2px then only x will be used. If py<2px then only y will be used.
Now py'=3py=6px=3px'>2px'. Hence after the price change only x will be used.
Since the output remains unchanged.
So q=x+2y=x'
Initial cost C=px.x + py.y = px(x+2y) = px.x'
Final cost C' = px'.x' = 2px.x'
C' = 2C
The cost exactly doubles and not more than double.

[Abhitesh]

Q1.pdf

[Rautparul]

Thank you for both answers and image also :)
Did you get where I went wrong in 3rd?

Also, I have 1 more query, if you can help with few other queries I'm facing:

1)A rm's production function is given by q = min{M,L^1/2} where M is the number of ma-
chines and L is the amount of labor that it uses. The price of labor is 2 and the price of machines
is 3 per unit. The rm's long run marginal cost curve is:
(a) a straight line with slope 4.
(b) upward-sloping and gets flatter as Q increases.
(c) upward-sloping and gets steeper as Q increases.
(d) a straight line with slope 2.
(e) a straight line with slope 3.

Answer: A


2)In the reclining chair industry (which is perfectly competitive), two dierent technologies of pro-
duction exist. These technologies exhibit the following total cost functions:
C1(Q) = 500+ 260Q- 20Q2 + Q3
C2(Q) = 1, 000+ 145Q- 10Q2 + Q3
Due to foreign competition, the market price of reclining chairs has fallen to 110. In the short run,
(a) rms using technology 1 will remain in business and rms using technology 2 will remain in business.
(b) rms using technology 1 will remain in business and rms using technology 2 will shut down.
(c) rms using technology 1 will shut down and rms using technology 2 will remain in business.
(d) rms using technology 1 will shut down and rms using technology 2 will shut down.
(e) more information is needed to make a judgment.

Answer: D


3) The snow removal business in East Icicle, Minnesota is a competitive industry. All snow-
plow operators have the cost function C = Q2 + 25; where Q is the number of driveways cleared.
Demand for snow removal in the town is given by Qd = 120-P. The long run equilibrium number
of rms in this industry is
(a) 11
(b) 22
(c) 14
(d) 120
(e) 23

Answer: B

[Abhitesh]

Assuming MP's to be marginal products. What is the justification behind assuming MP(S)/MP(L) = p_S/p_L? This  is correct though.
How does above implies  MP(S)/MP(L) = L/S = 1/9? Try to evaluate these for general function B=S^a. L^1-a for better understanding.
Third you have computed labour cost for producing juice only, you also need to add seed and labour cost to produce berries.
Q2.pdf

[Rautparul]

Yes, got my mistake. Thanks :)

[Rautparul]

True/False

A firm faces competitive markets both for its inputs and its outputs. If its long run supply curve is q = 3p; then it can not have constant returns to scale.

The answer is True. What is the logic behind?

[Rautparul]

Hi, I have doubt in this question. I got 2 prices as 4 and 2 but the answer is 3. Can anybody tell how?

Two firms constitute the entire doghouse industry. One has a long run cost curve of
3 + 4(y^2)/3) and the other has a long run cost curve of 10 + (y^2/10). If no new firms enter the
industry, at which of the following prices will exactly one rm operate?
(a) 1
(b) 3
(c) 5
(d) 7
(e) None of the above.

[Abhitesh]

Q3.pdf
Getting 40 for third part.

[Rautparul]

Thanks so much. :) :D

[Abhitesh]

Edit - For third question.
In long <C>=C' => Q+25/Q = 2Q => Q=5.
So each firm is willing to supply 5 units of removal.
Also in long run P=<C>=C'=10.
Q_d = 120-P =110.
Therefore 110 removals can be provided by 110/5 = 22 firms.