Q.Write the demand function, supply function, and consumption function in general algebraic form, and identify the independent and dependent variable in each.

State each function's standard linear form and name which variable is independent (input) and which is dependent (output) in each case.

Demand function: $Q_d=a-bP$, with price P as the independent variable and quantity demanded Q_d as the dependent variable. Supply function: $Q_s=c+dP$, with P independent and Q_s dependent. Consumption function: $C=a+bY$, with income Y independent and consumption C dependent.

Demand function: $Q_d=a-bP$, where $a,b>0$ are constants. Here PRICE (P) is the independent variable — it is treated as the variable that changes and to which quantity RESPONDS — and QUANTITY DEMANDED ($Q_d$) is the dependent variable, since it takes a specific value only once a value of P is given. The negative sign on $b$ reflects the (usual) inverse relationship between price and quantity demanded.

Supply function: $Q_s=c+dP$, where $c,d$ are constants (typically $d>0$). Again PRICE (P) is the independent variable, and QUANTITY SUPPLIED ($Q_s$) is the dependent variable. The positive sign on $d$ reflects the usual direct relationship between price and quantity supplied.

Consumption function: $C=a+bY$, where $a$ (autonomous consumption) and $b$ (the MPC) are constants. Here INCOME (Y) is the independent variable, and CONSUMPTION EXPENDITURE (C) is the dependent variable — the level of consumption is modelled as RESPONDING to the level of income, not the other way round.

In every case, the general pattern is the same: the variable that is taken as "given" or that the economic story treats as the driving cause is the independent variable, and the variable whose value is determined once the independent variable's value is known is the dependent variable.

Students sometimes assume price is ALWAYS the independent variable in every economic function — this is true for demand and supply, but for the consumption function it is INCOME that plays the independent-variable role; always check which variable the specific function's own story treats as the driving cause.