Grow 2% a year and living standards double in about 35 years. Grow 7% and they double in 10. Nothing dramatic happens in any single year, which is exactly why growth is so easy to ignore.
Learning objectives. After this week you can (1) explain why growth compounds and use the rule of 70; (2) name where growth comes from; and (3) compute a payback period for an investment.
Remember this: doubling time ≈ 70 ÷ growth rate. Small differences in growth become huge differences in wealth.
1) Growth compounds
Economic growth is a sustained rise in real GDP per person. It compounds: each year's gain builds on a bigger base. Real GDP of 100 growing 3% a year is 103 after one year and about 106.1 after two, not 106. For GDP per capita to grow, output must grow faster than population.
Years to Double ≈ 70 ÷ Annual Growth Rate (%)
At 2%: 70 ÷ 2 = 35 years. At 7%: 10 years. Country A grows 1.5% and doubles in about 47 years; Country B grows 3.5% and doubles in 20.
2) Where growth comes from
- Capital deepening: more capital per worker, like lifts, snow guns and groomers.
- Human capital: skills and training that make each hour of work worth more.
- Technology: better ways to combine labor and capital.
All three raise productivity, output per worker. The price of growth is investment, the "I" in GDP: output spent on building capital instead of consumed today. An economy that invests a bigger share grows faster later. Buying shares is a financial investment, not the "I"; only building productive capacity counts.
3) Depreciation: capital wears out
Machines and buildings wear out. Gross investment minus that wear is net investment, and only net investment grows the capital stock. At your resort the wear shows up as Deferred maintenance on your report; your decision form warns that the backlog builds into downtime and incidents.
4) Payback: does the investment earn its cost?
Payback Period = Cost ÷ Extra Earnings per Day
Your report shows your CapEx total, and the form says CapEx permanently improves capacity and satisfaction. CapEx comes out of your bank; if the bank can't cover it, the report says it was skipped. An $80,000 upgrade that brings $2,000 of extra revenue per full day pays back in 80,000 ÷ 2,000 = 40 full days. Extra capacity only earns on days when more skiers want to come than you can serve, and the cash you spend has an opportunity cost: whatever else it could have done.
Quick self-check
(a) An economy grows 5% a year. Doubling time? (b) A $60,000 investment earns $1,500 extra per full day. Payback? (c) GDP grows 2% while population grows 3%. What happens to GDP per capita? (Answers: 70 ÷ 5 = 14 years; 40 full days; it falls.)
Common mistakes
- Comparing an investment with one day's revenue. Compute the payback instead.
- Forgetting depreciation. Worn-out capital has to be replaced before you grow.
- Calling stock purchases investment. Only new productive capacity is the "I".
This week in the arena
Read your CapEx total and Deferred maintenance on your latest report. If your crew is weighing an investment, estimate the extra revenue it would bring per full day and work out its payback. How many days like that are left in your season?