This is the homework on Efficiency Concepts and why the partial equilibrium concept and the general equilibrium concept don't line up exactly, as well as the special case where they do. It's important to have a firm footing here because economic efficiency is our starting point in looking at organizations the M&R way. Then we can talk about various reasons for departures from efficiency.
If you have a question about this homework, please post it as a comment to this post.
I'm having trouble with General Equilibrium questions.
ReplyDeleteTo start I'm having trouble finding MRS at the intial allocation. I have tried dividing the y/x values given in the tables, and I'm not coming with the right answer.
Are you doing this first at A's allocation? A's allocation is given in cells B9 and C9.
DeleteYes, I have tried dividing the initial values of X and Y given in cells B9 and C9.
DeleteExactly what are you typing in cell B49?
Delete55/30
DeleteWithout an equal sign first?
DeletePlus are you using cell references?
55/30
ReplyDeleteI'm also confused on the algebra/equation that is needed to be used to find A's allcoation in a Pareto Optimal allocation
ReplyDeleteIf (xA,yA) is what A consumes, (xB,yB) is what B consumes, and (xW,yW) is the endowment for the whole economy, can you rewrite B's allocation in terms of the endowment for whole economy and A's allocation? That's the first part to finding the equation. The second part relates the MRS of A and the MRS of B at a Pareto Optimal allocation. You have to put those two together.
DeleteWith this explanation, I am still confused to find the A's allocation in a Pareto Optimal allocation.
DeleteWhat have you tried? I really don't want to give away the answer. I want you to work it through. If you can say what you tried, I can respond to that.
DeleteI have total endowment of (79,131). A's allocation is (26,87), which means B's allocation is (53,44). And, MRS of A is 3.34615 and B is 0.83019 with the MRS equation of y/x. Since A and B have same MRS equation, I used random variable i to relate MRS. Then, I don't know the next step.
DeleteSee my response below to Simon Kuznets. THE INITIAL ALLOCATION IS NOT PARETO OPTIMAL. You need to find another allocation that is. What must be true about the MRS of the two agents at a Pareto Optimal allocation?
DeleteDid any of you figure it out? Very much struggling right now!
DeleteI am struggling on Pareto Optimal Allocation too.
ReplyDeleteI found B's allocation which is (82,50) and found MRS of A and B which is 2.414634 and 0.609756.
Now how do I put those together?
The initial allocation is not Pareto Optimal. The difference in the MRS of the two agents means there are gains from trade. Since A's MRS is greater than B's at the initial allocation, a Pareto improving trade will have A buy a little of Good X from B while paying for it with Good Y, at a relative price that is somewhere in between the MRS of the two agents.
DeleteAt a Pareto Optimal allocation, there are no more gains from trade.
Okay, I think B's allocation is (162,25.757576)?
DeleteLet me remind you that when you enter your answers into the Excel, use cell references, which are exact, not decimals that are only approximate. I also want to note that there are many Pareto Optimal allocations, not just one.
DeleteYou need to do some pencil and paper calculations that amounts to high school algebra - two linear equations in two unknowns, reduced down to one equation in one unknown. I will not do that algebra here. You might figure it out yourself.
ReplyDeleteHi, I'm having trouble finding A's allocation in a Pareto Optimal allocation. From the previous comments I figure that my first step should be figuring out what the Pareto Optimal is, which I'm not quite sure how to do. I know that the MRS of the two agents should be equivalent for Pareto Optimal.
ReplyDeleteI'm only seeing this in the morning. A different constrain on you is that after about 6 PM, I'm offline for the rest of the evening.
DeleteMRS A = yA/xA. MRS B = yB/xB. So, as you noted, these two must be equal at a Pareto Optimal allocation. Also, the allocations for A and B must add up to the total endowment for economy. So
xA + xB = xTotal and yA + yB = yTotal. Use that fact to solve for B's allocation in terms of the total allocation and A's allocation. Then substitute back into the equation that says the two MRS are the same. This should give you one linear equation that expressed yA in terms of xA.
This is high school algebra. Nothing more.