Comments on Problem Set #4

Problem 1: First of all, don’t be too confused about the equations:

In class I had M x V = P x Q, where Q was real output.

The equation as in the book (p. 357) uses Y instead of Q as real output.

Why the difference? Not to intentionally confuse you. Q and Y are both commonly used to represent real output. Traditionally, the quantity equation used Q rather than Y. But in our text and usually in my notes we use Y as real output.

Now, for the tough part:

For B through D, you should take the easy way out. Make use of that quantity equation in percent change form:

Δ%M + Δ%V = Δ%P + Δ%Y

So when it says velocity is constant then Δ%V = 0%. Also, price stability means Δ%P = 0%.

In parts B, C, and D, you should assume that Δ%Y is 5%. So for each, you just assume Δ%V = 0% and Δ%Y = 5%, and you need to figure out Δ%M and/or Δ%P. Make sure that equation balances. That means if the left hand side sums to 0%, the right hand side must sum to 0%. If the left hand side sums to 20% the right hand side must sum to 20%.

Clues that you did it right: For B, your answer should be a negative price change. For D you should have double-digit money growth. Just figure out what those percentage changes are.

If you feel so bold you can take the values in A and alter them by the percentage changes you calculate to find the dollar values. However, you’ll get full credit if you merely present the answers in percentage changes.

Problem 2

This is related to the quantity equation from problem 1. You should use the version in percentage change form to help answer this. This is a more generalized version of 1-C. This is not a hard question, it’s really just an algebraic question with an economic policy implication.

Problem 4

For part C, “sticky-wage theory” is discussed on p. 443. It pertains to the slow adjustment of AS_SR to the long run equilibrium.

Problem 6

A. You must start with a short run disequilibrium. So when AD and AS_SR cross, it is at less than full employment.

C. Use the money market model we discussed in class. It is also depicted in Figure 3, p. 466. You can see from that diagram how changes in the money supply change interest rates and then change Aggregate Demand.

Problem 7

Some people were taken aback by the derivation of the multiplier in class. Two comments:

i. You will NOT have to know how to derive those multipliers.

ii. So why did I talk about it? Because your book does a lousy job explaining where that comes from. Honestly, if you did not think that the algebra we did in class today was “simple” then you need to take more algebra. That was a simple problem and a simple argument. When the book derives it by saying that 1/(1-b) is the sum of an infinite series, you should find that much more difficult than the algebra we did! (See page 471.) I used “b” in class because it was easier than writing MPC all the time. My “b” is Mankiw’s MPC. I think you would find this much more interesting the more curious you are. Curiosity makes education a rewarding experience. If you’re not a curious person, college can be quite a drag. The economy is a complex system. You should be curious as to how it works.

iii. Yes, you do need to understand what we mean by marginal propensity to consume (MPC) for the test.