help S2000magician and others: three rather detailed questions about CFAI economics in CFAI book

This is for everyone but I’m a huge fan of S2000magician so I hope he chimes in too. Forgive me but I’m a former journalist with no business training and now work in the finance industry and besides passing the test, I just want to learn this stuff. It’s interesting. Here are three questions that have stumped colleagues, classmates and our teachers…

  1. page 487 with regards to forward premium or discount: The domestic currency will trade at a forward premiu (F f/d > S f/d) if, and only if, the foreign risk-free interest rate exceeds the domestic risk-free interest rate.

The formula appears above this sentence. I get this from the formula but I don’t understand the logic behind this. Why should the DOMESTIC currency trade at a forward premium when investors are getting more interest from the foreign currency? So if the € pays 3% and the $ 1%, why wouldn’t the € appreciate, at least in the short term, and thus trade at a forward premium?

  1. page 616…can someone explain how they go from y=Y/L=AK^ α to the equations that follow that including

∆k/k=∆K/K - ∆L/L…

A friend with a Master’s in Financial Engineering said he though they were doing partial derivatives here, which of course, they don’t even mention or explain…Anyone want to take a crack at this and the formulas that follow on page 616?

  1. page 636: Depending on global aggregate demand conditions, wages might even have to fall in the developed countries in the process of shifting wealth and income to the developing economies (understood by questioner here). Because of the surge in the global supply of labor, the overall share of labor in global income should decline relative to capital.

Question: If you have a surge of labor, thus more people working, why in the world would you have labor’s share of global income decline relative to capital??

Many thanks!!!

If EUR is earning 3% and USD is earning 1%, then you might be willing to pay more USD for EUR today (so that you can earn that extra 2%), but why would you pay more USD for EUR in the future, after the EUR has earned the additional 2%? You missed your opportunity.

That’s what’s really happening here. USD is worth more EUR because the EUR interest rate is higher, but EUR is worth fewer USD. Perhaps you can think of it like the price of a stock (EUR) after it goes ex-dividend: you pay less (USD) for it because you missed the opportunity to get that additional cash flow.

We start with

k = K/L

Next, we take natural logararithms:

ln(k) = ln(K/L) = ln(K) − ln(L)

Finally, we compute differentials (not exactly partial derivatives – for one thing, we don’t have a separate independent variable here – but very similar), noting that the differential of ln(x) is dx/x ≈ Δ_x_/x:

Δ_k_/k = Δ_K_/K – Δ_L_/L

Similarly, for

y = Ak^α

ln(y) = ln(Ak^α) = ln(A) + ln(k^α) = ln(A) + _α_ln(k)

Δ_y_/y = Δ_A_/A + α_Δ_k/k

I believe that the point they’re trying to make is that you have a surge of labor in low-wage countries, lowering the global average wage, and lowering the share of labor relative to capital.

Many you’re welcomes.

S2000 Magician, you are AWESOME!!! Thank you:)

My pleasure.

s2k is awesome

s2k has too much free time on his hands.