Budget Constraints

[ascapa]

Hello,

We have learned a ton of different budget constraints now, and it is hard to keep them clear in my head. Is there a way we can add a document that clearly labels each budget constraint for each type of problem and labels the what the variables are? I feel like that would be super helpful. Thanks for the help.

[Lindsay Appell]

Hi ascapa!

Great idea, let's get that started here! I'm going to include a template below and then you and other students can start filling in the different parts! I'll check it over and confirm that everything is correct.

MIDTERM 2 BUDGET CONSTRAINTS:

1.     Recreation and Consumption:

2.     Present and Future Consumption:

          When m1 and m2 are in real terms:

               -Present value:

               -Future value:

          When m1 and m2 are in nominal terms:

               -Present value:

               -Future value:

3.     Insurance:

Let me know if you have any questions!

-Lindsay

[J]

Haha, way to not just hand it to us. 

1.     Recreation and Consumption:

• pC + wR = M + wL(bar)
• Recall that usually, p=1 (aka p is unity). When we solve for a maximum by comparing the MRS to the price ratio, MRS = w/p. But since p is unity aka 1, this just simplifies to MRS = w.
• So your function will probably end up looking like
• C + wR = M + wL(bar)

Recall that 

• C = consumption
• R = recreation (known as Le in older problems)
• M = non-wage income (known as Yn in older problem, or Y(not))
• w = wage, what you earn when you work, and also the cost of recreation (because you forgo wages if you work)
• L(bar) = total time available to use as work or leisure = R + L
• L = labor
• p = 1 (unity)

2.     Present and Future Consumption:

          When m1 and m2 are in real terms:

               -Present value:

• c1+c2/(1+p) = m1 + m2/(1+p)
  

               -Future value:

• (1+p)c1 + c2 = (1+p)m1 + m2
• Note that p is rho, not price. I italicized a normal p to make it resemble a rho symbol more.
• p = real interest rate
• r = nominal interest rate
• pi = inflation
• p = (1+r)/(1+pi)

          When m1 and m2 are in nominal terms:

               -Present value:

• c1 + c2/(1+r) = m1 + m2/(1+r)

               -Future value:

• (1+r)c1 + c2 = (1+r)m1 + m2

3.     Insurance:

I'm gonna use an italicized y, y to represent gamma.

[(y/(1-y)]Cb + Cg = M + [(y/(1-y)](M-L)

• Cg = consumption in the good state
• Cb = consumption in the bad state
• y = the per $ cost of accident insurance
• M = total wealth
• L = The cost of the loss
• K = the $ amount of insurance that can be bought (less than L)

[Lindsay Appell]

All of the budget constraints and explanations look perfect! For recreation and consumption, although price will usually be 1, I would recommend always using the budget constraint and price ratio with p in it. Then, if they did make the price something other than 1 on the test, you wouldn't need to adjust your method.

[J]

Good point! Actually, the problem you gave us where p=2 in the problems we went over in the Review Session, was the first time I've ever seen p be anything other than unity. In any case, be ready for anything. 

[Lindsay Appell]

Exactly! Although some situations may be rare, it's always good to know how to handle them if they come up on the test! Plus, it will make you all the more prepared for the easy questions :)