Conceptual Doubts from Q 1-20-DSE 2011

[Erika]

I am currently solving the 2011 paper, which is the first paper Im solving. I have a great deal of conceptual difficulties both in theory and numericals. Im posting my question in parts and if one can explain the working (or theory), I would be really grateful :) only a month left. :/ starting to worry now

Q1. How is x-1 local min? I read through other answers and differentiated the func four times but still didnt not get f(x) > 0 for being a min. Please help me understand!

Q2. How do we go about mapping a func as given: f(x,y)=(x-y,x+y) and find its range?

Q3. What is the idea behind solving this one? I mean to put- which topic is this under and how do we get 2 as the min number of scalars? If someone could give me the working solution.

Q6. In my opinion, it shoud be (d) 'both a and b' while the ans key says (b). I justified mine saying 20 is definitely less REPRESENTATIVE of all MA students, thus the error in calculation of mean. Although when one goes from 20 to 30 students, the PRECISION increases and the sample becomes more representative.

So, which logic is correct. If mine is wrong, kindly give logic to only (b) being correct.

Q10. Given the demand and cost function, number of firms, price=p; how do we calculate the equilibrium price?? (I tried looking this up online but there isnt any solution with exact same given info)

Q11. Similar doubt as above. How do we calculate the eqm price change? What topic this falls under and which formula do we use?

Q 12. How do we go about calculating profit maximising price for a monopolist with an inverse demand function?  I considered MC=20 and p=60.2q (given). if w differentiate MC it gives 0...which is mot minimising costs. .?

Q13. I understand this question is not based on any trick but simple theort. Which topic should i cover to strengthen this one? or if there trick in this question which need more application than theory??

Q16 and Q17. how does ISLM change with change in income and increase in inflation?? i have the answers with me but need to understand the concept.  

Q18. Im very confused with the logic of devaluation in currency and its effect based on elasticities of x and m....giving example in rupees can someone please explain how (c) is correct?



I know these are MANY questions. But i really do need help. Any help is appreciated and I am sure it'll help other readers as well. In the mean time im going to buy DU BA eco books and read them through. Also Ill post doubts from Q21-60; the ones I still dont get after reading the discussions.

Thanks and cheers!!

[duck]

Hi.. :)

1) Use higher order derivative test. f''''(x) = 24>0.

2) Eg: x=0, y=1 then f(x,y) = f(0,1) = (-1,1).
Its easy to find its range.

3) Given v1, v2, ...vn are linearly dependent vectors...That is:
c1*v1 + c2*v2+...+cn*vn = 0 such that not all scalars (c1,c2..cn) are zero.
Now, suppose only c1 ≠ 0 and rest all are zero then, we'll have c1*v1 = 0 but this cant be possible as c1≠0 and v1 is a non zero vector. Hence, minimum number of non zero scalars = 2.

10) Each firm would like to supply: q=p/2 (Use P=MC)
Therefore, market supply Q=10*p/2 = 5p and Market demand=100-15p
Solve them you'll get p=5.
[They're asking you to find Short run Competitve equilibrium]

11)New supply: Q=20+3(p-10) ; Demand=100-p.
Equate Demand and Supply, you'll get p=27.5
Therefore, change in p= 27.5-20 = 7.5
[Its simple demand and supply question with impostion of taxes]

12) Find TR by multiplying "q" on both sides of inverse demand function.
Find MR and equate it with MC.
You'll get p=40

13) Read Stackelberg model.

16) Y=cY+I(r) where c=Marginal propensity to consume and Investment(I) is a function of rate of interest(r) and is negatively related with r.
⇒ Y = I(r)/(1-c)
⇒ SLope = dr/dy =1-c
Now, if c increases.  Slope decreases. This make IS flatter.

17)leave the LM curve unchanged (assuming that we are plotting it in (Y, i)−space where Y is income and i is nominal interest rate)

18) Marshal lerner condition.

[Erika]

Thanks a LOT duck  you single handedly solved most of the doubts.
Im glad this forum is going to be of good help. if not this year then next :)

Q6 logic explanation left, if anyone could help :)

Regards.

[Erika]

hi @duck...correct me if you feel otherwise, but i think we should add the tax in ques 11  although the ans (diff of rs 7.5) remains the same.
It is the consumers who pay the final tax imposed on goods. thus, the price of good increases as result of sales tax .
BUT. the question says...increased by ..? confused here, why rs 10 should be deducted from price.

Also, for ques 12, i get q=1/12. thus, p=10. How do you get 40?

[anon_econ]

The expected value of the sample mean is the population mean, regardless of sample size. So the sample mean is an unbiased estimator of the population mean. Don't try to get into the intuition of the terms 'more bias' and 'less representative'; bias is a statistical term

[anon_econ]

How do you get q=1/12?

[Erika]

Ok.. Thats great! I missed focusing on 'random sample'  

I get 1/12 this way:

TR= P* Q = 60*2Q *Q =120 Q^2

MR = TR' = 240 Q

MC = 20. Equating the two.

240 Q=20
Q= 20/240 = 1/12

P= 60 * 2Q = 120 (1/12) =10.

[anon_econ]

Uh-oh. p=60-2q.

[Erika]

damn!! Xeroxed version didnt print well i guess :/ thanks ..makes my day simpler ;)

[duck]

hey.. its not about getting the answer. Its about doing the question properly.
If you add tax in the supply, it doesn't make sense. Because by imposition of taxes, seller gets a lower price than before. So, whatever price he was getting earlier, now he gets less price now.

Eg: Suppose, demand price =p and supply price is p'.
[Note: By demand price, i mean the price which consumer needs to pay. And Supply price:the price that the seller gets.]
Before imposition of taxes, we must have p=p'.
But after imposition of  tax , consumer pays p=p'+t.
Or p'=p-t.

Its like seller would now receive a lower share of price as he needs to pay tax to the govt. Similarly, consumer needs to pay a higher price as he needs to pay tax. What burden of tax is imposed on seller and buyer can be easily calculated.

For eg: In this case, after tax : p=27.5 and p'=17.5 So, the tax burden is shared as: buyer is paying 7.5 extra and seller is getting 2.5 less.