Show That for the Following Regression Model
Y_t = ${ } _ { e } \beta _ { 0 } + \beta _ { 1 \times t + u }$

question 14

Essay

Show that for the following regression model
Y_t = ${ } _ { e } \beta _ { 0 } + \beta _ { 1 \times t + u }$ where t is a time trend, which takes on the values 1, 2, …,T, β₁ represents the instantaneous ("continuous compounding")growth rate. Show how this rate is related to the proportionate rate of growth, which is calculated from the relationship
Y_t = Y₀ × (1 + g)^t
when time is measured in discrete intervals.

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Definitions:

Excise Tax

A tax levied on specific goods, services, or transactions, such as tobacco, alcohol, and fuel, usually to discourage consumption or raise government revenue.

Supply Curve

A graphical representation of the supply schedule, showing the relationship between quantity supplied and price.

Demand Curve

A graphical representation of the demand schedule, showing the relationship between quantity demanded and price.

Equilibrium Quantity

The quantity of a good or service bought and sold at the equilibrium (or market-clearing) price.