Help with Microeconimcs / Quantitative Economics Question please...

[Jackass]

Hi, just trying to do some revision problem sets and I just wanted clarification on if I'm going in the right direction. I posted similar in the Economics forum, but it's not very active and not sure if it's geared towards actually quantitative discussion / calculations, so perhaps this forum is more appropriate?

So I have one question:

Qd = 1800 - 2P(squared) + 4P
Qs = 3P(squared) + 4P - 200

Question is what is elasticity of supply in equilibrium?

So I put Qd = Qs and solve P as 20 and Qd and Qs both as 1,080

My problem is now finding the elasticity of supply

Do I manipulate Price in this instance? So let P = 30 and I get Qs = 2,620

%changeP = 0.5% and %changeQs = 1.43%

%changeQs/%changeP = 2.86 and this is the elasticity of supply?

The only reason it's throwing me is that it is giving multiple choice answers of A) 62/27 or 2.296 20 C) 1/54 or 0.185 D) 1080 or E) None of the above

I would go with none of the above, but am thrown by it if I can't match the answer!! :shock: I'm just not sure if above method is finding price elasticity or supply elasticity, as if I was to manipulate supply number I'm not sure how to go about it...

Ok, a second one (and I really should know this, but am rusty as hell)

Qd = 900 - 3P
Qs = 2P - 100

If tax of 25 is introduced, how much Revenue will Government earn?

So I solve P = 200 and Qd and Qs = 300

So I solve Qs as 2(P-T) - 100 (from given equation)
Qs = 250

And then multiply Qs with tax (250) by T (25) and get 6250 as Revenue, however, once again, this is not one of the options on the multiple choice, with answers given as A) 1850 7,500 C) None of these D) 4625 E) 6750

Care to let me know if I'm doing it right or where I'm going wrong please?

Also, how do I calculate who would bear the burden of tax? IIRC, it is always shared jointly between Consumer and Supplier? Is this the case, or can it be entirely on the Supplier or the Consumer, and if it can differ, how do I calculate this?

Thanks a million for help, was sick last week so trying to catch up with what I missed.

Cheers.

hivizman

[Jackass] wrote: »

Hi, just trying to do some revision problem sets and I just wanted clarification on if I'm going in the right direction. I posted similar in the Economics forum, but it's not very active and not sure if it's geared towards actually quantitative discussion / calculations, so perhaps this forum is more appropriate?

So I have one question:

Qd = 1800 - 2P(squared) + 4P
Qs = 3P(squared) + 4P - 200

Question is what is elasticity of supply in equilibrium?

So I put Qd = Qs and solve P as 20 and Qd and Qs both as 1,080

My problem is now finding the elasticity of supply

Do I manipulate Price in this instance? So let P = 30 and I get Qs = 2,620

%changeP = 0.5% and %changeQs = 1.43%

%changeQs/%changeP = 2.86 and this is the elasticity of supply?

The only reason it's throwing me is that it is giving multiple choice answers of A) 62/27 or 2.296 20 C) 1/54 or 0.185 D) 1080 or E) None of the above

I would go with none of the above, but am thrown by it if I can't match the answer!! :shock: I'm just not sure if above method is finding price elasticity or supply elasticity, as if I was to manipulate supply number I'm not sure how to go about it...

The way you have gone about calculating elasticity works exactly only when your supply function is linear. But you have a quadratic supply function. In this case, it's worth remembering that there is an exact mathematical formula for elasticity:

Elasticity = (dQ/Q)/(dp/P) = (dQ/dP)x(P/Q)

The first term in the first expression is the proportionate change in quantity demanded given a small proportionate change in price. When rearranged, the term dQ/dP can be interpreted as the first derivative of the function Q, so we can calculate it by differentiating the function Qs = 3P^2 +4P - 200 to qet dQ/dP = 6P +4. Substituting Q = 1080 and P = 20 will give you one of the answers offered.

If you were to work out what would be the change in supply for a 1% fall in price, you could calculate Q for P = 19.8. This gives Q = 1,055.32, representing a fall of 2.28%. This is very close to one of the answers, and if you use the mathematical formula you will get that answer exactly.

[Jackass] wrote: »

Ok, a second one (and I really should know this, but am rusty as hell)

Qd = 900 - 3P
Qs = 2P - 100

If tax of 25 is introduced, how much Revenue will Government earn?

So I solve P = 200 and Qd and Qs = 300

So I solve Qs as 2(P-T) - 100 (from given equation)
Qs = 250

And then multiply Qs with tax (250) by T (25) and get 6250 as Revenue, however, once again, this is not one of the options on the multiple choice, with answers given as A) 1850 7,500 C) None of these D) 4625 E) 6750

Care to let me know if I'm doing it right or where I'm going wrong please?

Also, how do I calculate who would bear the burden of tax? IIRC, it is always shared jointly between Consumer and Supplier? Is this the case, or can it be entirely on the Supplier or the Consumer, and if it can differ, how do I calculate this?

Thanks a million for help, was sick last week so trying to catch up with what I missed.

Cheers.

The important thing to remember is that there will be a new equilibrium. If the suppliers cut output to 250 units, customers will be willing to pay more than the previous equilibrium price.

So you need to calculate the equilibrium where quantity demanded equals quantity supplied. If P is the price paid by customers, and P - 25 is the revenue received by suppliers, then we have:

Qd = 900 - 3P
Qs = 2(P - 25) -100

Solve the equation 900 -3P = 2(P - 25) - 100, work out the new Q, and multiply this by 25, and you will get one of the answers on offer.

First question: answer is A; second question: answer is E.

[Jackass]

Thanks a million for that. Turns out I was going completely wrong way about it. Notes given aren't very good, but your explanation helps a lot, thank you! Looks like I've a lot of practice to do