Hi I am looking for some pointers with an economics problem.I have no background in economics and find it easy to get to contradictory arguments.Basically, the situation is there are two goods, A and B, the supply of which is completely insensitive to price.Demand for them, however, follows normal arguments (reducing at high prices).The complicating feature is that the supply for the two is fixed but it's trivial and costless to convert one to the other.How could one frame this example as a economic problem.I am particularly interested in how the demand for B effects the price of A (and vice versa).This isn't homework or anything like that, it's a very simplified description of a couple of assets that sounds a little like the Giffen goods sort of situation (which I could never really work out).Any ideas?Cheers

Hi tw,"it's trivial and costless to convert one to the other" means that the products are perfect substitutes? In this case, shouldn't Price of A equal Price of B on a No-Arbitrage argument?..maybe I am missing something...

I agree with chocolatemoney. Prices of A and B should be equal. Their price will adjust to match aggregate demand and aggregate supply.

Thanks chocolatemoney & maratikus.I'm not disagreeing with your conclusion on the prices, just looking to frame the problem propertly so all these conclusions drop out(not sure if arbitrage is the right concept for these economic problems).Here's what I was thinking.The supply of A & B are sA & sB, fixed such that sA + sB = sToT (independent of prices, with sToT fixed).Price of A adjusts to demand of A as pA(dA) and similar for BDemand = supply for A and B independently means pA(dA)= sA and pB(dB)=sB.Hence pA(dA)+pB(dB)= sToTTaking the demands to be the independent variables would suggest (a) pA <> pB (b) and d (pA)/ d(sB) < 0Where's the flaw in the argument?QuoteOriginally posted by: maratikusI agree with chocolatemoney. Prices of A and B should be equal. Their price will adjust to match aggregate demand and aggregate supply.

Given the assumptions (fixed supply of A and B, products perfect substitutes), I think the demand for A is linked to the price of A and B.Here what an "economic agent" would do in such a case: if I need A and Price(B) < Price(A), I'd buy B until the additional demand for B shifts brings P(B) to be equal to P(A)If the market is efficient enough, we can use P(A)=P(B) and there's no need to model the prices for A and B; we can just look at the aggregate demand:sA+sB=sTotdA+dB=dTotas said by maratikus.If you would like to model how a no-arb price level is reached, I guess you have to model a system where the demand of a product is linked to the price and supply of the other.

QuoteOriginally posted by: chocolatemoney ....If you would like to model how a no-arb price level is reached, I guess you have to model a system where the demand of a product is linked to the price and supply of the other.Any ideas how this is done? Basically the gist of what I'm after is, from purely economic arguments, if the demand of one product increases what happens to the price of the other?

This all depends on what you are trying to model. It is important to remember that assets do not economically hold the same properties as goods. Some things (such as housing) are both assets and goods, however I am going to assume that you are referring to goods. I suspect that you are confusing transaction costs with substitutability. Transaction costs are the (irredeemable) resources lost when a certain economic action is required. An example of this would be the gas burned going to buy groceries at the store. Regardless of whether you decide to purchase anything, the gasoline is a sunk cost. Substitutability is how similar two goods are in providing a person's utility. an example of substitutable goods are a car and a bike in providing transportation. the price of one influences the price of the other because, at the margin, the consumer decides whether he/she wants to use either as a means of transportation. an eraser and a car are not substitutable. The relative price of one has no influence on the price of the other. Another thing you should consider is the income effect. As the relative price of some goods change, you drop in income (or rise) will change the preferences of the basket of goods that you will want to consume. an example of this is food. as you get richer, you will spend proportionately less on food. Therefore, if the price of rice were to drop, you may actually consume less of it!! It depends on the magnitude of the income and substitution effects. A giffen good is extremely rare and has only been documented in a few papers (one was corn in Mexico). This is a good that as the price rises, you will consume more of it. That is the income effect dominating the substitution effect. I suspect that what you are examining is not a giffen good as finding one would immediately place you in the top econ journals. To summarize, it depends on how your model consumer is supposed to behave. I know this doesn?t help much, but I hope this will clarify some things for you.

QuoteOriginally posted by: twHi I am looking for some pointers with an economics problem.I have no background in economics and find it easy to get to contradictory arguments.Basically, the situation is there are two goods, A and B, the supply of which is completely insensitive to price.Demand for them, however, follows normal arguments (reducing at high prices).The complicating feature is that the supply for the two is fixed but it's trivial and costless to convert one to the other.How could one frame this example as a economic problem.I am particularly interested in how the demand for B effects the price of A (and vice versa).This isn't homework or anything like that, it's a very simplified description of a couple of assets that sounds a little like the Giffen goods sort of situation (which I could never really work out).Any ideas?CheersYou' dhave to start with preferences and then derive demand functions from them. Let's ay income is Y, prices are PA, PB. then a simple demand fucntion for perfect subsitituites would be XA = 0 if PA >PB, and Y/PA if PA < PB. Onc eyou have the deman functions you'd have to equate these with Supply (say SA and SB) to find equilibrium price: XA(PA,PB) = SA*PA.