Macroeconomics — Unit 2: Investment Function and Investment Feasibility

🏭 In macroeconomics, investment (I) is expenditure on expanding the economy's productive capacity: buying machinery and equipment, constructing buildings and infrastructure, increasing firm inventories. This differs from the everyday meaning of "investment" in financial markets.

📉 There is an inverse relationship between the interest rate and investment: interest rate ↑ → investment ↓.
A high interest rate makes financing more expensive (loans) and raises the opportunity cost (forgone return from bank deposit).

📊 I = I_B + I_G
Total investment includes: business investment (I_B) — by firms; public investment (I_G) — by the government (roads, bridges, public buildings).
Note: "gross investment minus depreciation" is the definition of net investment.

🔧 Net investment = Gross investment − Depreciation (I = GI − D)
Net investment measures the true addition to the capital stock, after deducting the wear and tear of existing capital.

😊 There is a direct relationship between expectations and investment: optimistic expectations → investment ↑. If firms expect a good economic future, they will want to expand productive capacity to meet expected future demand.

📈 The signs indicate the direction of influence:
• r⁻ = interest rate has an inverse effect (interest rate rises → investment falls)
• expectations⁺ = direct effect
• Y⁺ = output has a direct effect

🔄 On the investment curve graph (r on the Y axis, I on the X axis): movement along the curve occurs when the interest rate changes. A change in expectations or output causes a shift of the curve.

📌 Autonomous investment (I₀) is the part of investment that does not depend on output. It is influenced by: expectations, technology, government policy. Unlike induced investment which depends on Y.

💹 Present Value (PV) is the value in today's terms of a sum to be received in the future.
PV = A/(1+r)ⁿ
This allows future receipts to be compared with present expenditures.

🧮 Solution:
PV = 1,210/(1.10)² = 1,210/1.21 = 1,000 ILS
That is, 1,210 ILS in two years is worth 1,000 ILS today (at 10% interest).

📊 NPV = Sum of PV of receipts − Investment cost
NPV = Σ[A/(1+r)ⁿ] − Cost
The tool for investment viability: NPV > 0 = worthwhile; NPV < 0 = not worthwhile.

✅ Solution:
PV = 11,000/1.05 = 10,476.19
NPV = 10,476.19 − 10,000 = 476.19 > 0
Since NPV is positive, the investment is worthwhile.

📉 There is an inverse relationship between the interest rate and NPV. A rise in the interest rate reduces the present value of future receipts (the denominator grows), so NPV falls.

⏱️ The shorter project is preferred because the receipts arrive sooner, so their present value is higher (divided by a smaller denominator). The NPV of the shorter project is higher.

💡 When the interest rate is low, the NPV of every project rises (future receipts are worth more today). Projects that were not worthwhile at a high interest rate become worthwhile at a low rate.

🧮 Solution:
PV = 1,000/(1+0)⁵ = 1,000/1 = 1,000
When the interest rate is zero, there is no time discounting — money today is worth exactly the same as money in the future.

🔄 Discounting is the calculation operation that brings future receipts to their present value (in today's terms). This allows a present expenditure to be compared with future receipts.

📊 When there is a constant ratio between costs and receipts (here 1:2), the same ratio applies to NPV.
NPV(A) = 150/(1+r) − 100
NPV(B) = 300/(1+r) − 200 = 2×NPV(A)

🏦 A fall in the interest rate increases investment: financing costs fall; more projects become worthwhile (NPV rises); the opportunity cost of investing falls. This is the inverse relationship between r and I.

🧮 Solution:
PV₁ = 11,000/1.1 = 10,000
PV₂ = 11,000/1.21 = 9,090.9
Total PV = 19,090.9
NPV = 19,090.9 − 20,000 = −909
Negative NPV → not worthwhile to invest