Equations till midterm 1

Production Function

Y = A(K^(1/3))(L^(2/3))

Shows how much output/GDP the economy produces.

Y = output/GDP

A = productivity (TFP)

K = capital

L = labor

More A, K, L → more output.

Resource Constraint

Y = C + I

Everything the economy produces is either consumed or invested.

Y = output/GDP

C = consumption

I = investment

Investment Equation

I = sY

The economy invests a fixed fraction of its output.

I = investment

s = saving/investment rate

Y = output

Example: s = 0.20 means 20% of output is invested.

Depreciation eqaution

Depreciation = δK

Shows how much existing capital wears out each period.

δ = depreciation rate

K = existing capital

Example: δ = 0.10 and K = 1,000 → 100 units depreciate.

Capital Accumulation

ΔK = I - δK AKA ΔK = sY - δK

Shows how much the economy's capital stock changes.

ΔK = change in capital

I = new investment

δK = capital that wears out

Investment adds capital; depreciation removes capital.

Capital Next Period

K(t+1) = K(t) + I(t) - δK(t)

Next period's capital = current capital + investment - depreciation.

K(t) = capital today

K(t+1) = capital next period

Steady State CONDITION

ΔK* = 0

here,capital is no longer changing.

Steady State

sY* = δK*

here, investment exactly equals depreciation.

Investment = capital being added

Depreciation = capital being lost

Since additions = losses, total capital does not change.

Unemployment rate

(Unemployment/ labor force) x 100

Balance sheet

Assets= Liabilities + Equity

Equity

Assets-Liabilities

Capital/ asset ratio

Equity/ Total Assets

Assets to reduce

Current assets − Maximum allowed assets