Unraveling the Marginal Propensity to Consume (MPC): Its Relationship with Consumption and Income

Decomposing Straight Line Direction Coefficients in Linear Functions: Interpretation of Change in Y with Change in X Name: Alvinska Hebat Grade: 910-Math Description of the Straight Line Direction Coefficient on a linear function Y=a + mX • • • • • m = ΔY/ ΔX = straight line direction line coefficient m can be described verbally as follows: if there is an increase in X by 1 unit (Δ X =1) then Y will increase by m units (ΔY = m), and if X decreases by 1 unit (Δ X = -1). then Y will decrease by m units (Δ Y = -m). Then "m" is the ratio between the increase in Y to the increase in I unit of X, or the ratio between the decrease in Y to the decrease in I unit of X so that m = ΔY/ΔX = m/1 or = m/-. 1. Example: 1. Y = 2 + 3X we describe as follows: if X increases by 1 unit (ΔX = 1) then Y will increase by 3 units (ΔY = 3) or if X decreases by 1 unit (ΔX = -1) then Y decreases by 3 units (ΔY = -3) so that the coefficient of direction of the line (m) = 3/1 or -3/-1 = 3. 2. Y = 4 - 2X we describe as follows: if X increases by 1 unit (ΔX=1) then Y will decrease by 2 units (ΔY=-2) or if X decreases by 1 unit (ΔX=-1) then Y increases by 2 units. The concept of "marginal" in Economics In general, the concept of "marginal" indicates the ratio between changes in one variable and changes in another. Marginal concept in economics: • • • • • • • Marginal Propensity to Consume (MPC) = ratio of change in consumption to change in income (ΔC/ΔY) = slope of the consumption function: C = a + bY. So MPC = b. Marginal Propensity to Save (MPS) = the ratio of changes in savings to changes in income (ΔS/ΔY) = the slope of the savings function: S = -a + (1-b)Y, so MPS = (1- b) Marginal Physical Product of inputs (MPPi) = the ratio between the change in total production and the change in the number of inputs (ΔTP/Δi) = the slope of the total production function: TP = a + βi, so MPPi = β Marginal Revenue (MR), the ratio between changes in total revenue (TR) and changes in output (ΔTR/ΔQ) = the slope of the total revenue function TR = PQ; then MR = P Marginal Rate of Substitution (MRS), the ratio between the changes in the respective quantities of goods consumed (ΔQy/ΔQx) = the slope of the Indifference function; Qy = φQx; then MRS = φ Marginal Rate of Technical Substitution (MRTS)) the ratio between the change in each input amount to produce a certain level of product (ΔK/ΔL) = the slope of the isoquant function: K = a + μL, then MRTS = μ Marginal Utility (MU) the ratio of the change in total satisfaction (TU) to the change in the amount of goods consumed (ΔTU/ΔQ) = the slope of the total satisfaction function: TU = ψQ, then MU = ψ lOMoARcPSD|26370826 Concept of Point Elasticity • • • Point elasticity measures how much a particular variable responds to a change in its cause variable at a given level of that variable. So point elasticity is the ratio of the change in the dependent variable to the change in the independent variable at a certain point or value. Elasticity concepts known in economics are price elasticity of demand/supply, income elasticity of demand, cross-price elasticity of demand, etc. Point Elasticity of Linear Functions with One Free Variable If Y = f (X) = a + mX; then in general, the elasticity of Y with respect to X (E) is the ratio of the change in Y to the change in X. The coefficient of elasticity of Y with respect to X is expressed mathematically as follows: