Demand and Supply Shocks: Comparative Statics and Linear Models

Comparative Statics: Demand and Supply Shocks

  • Goal of the micro intro: develop intuition for macro models by understanding how equilibrium moves in response to exogenous shocks and why. Distinguish how demand and supply respond to shocks.

  • Key distinction: demand shock vs price movement

    • Demand shock: shifts the entire demand curve (change in demand). For every price, a new quantity is demanded. This is a shift of the curve.

    • Price movement along the supply/demand curve: change in quantity supplied/demanded when price changes, holding the curve fixed. This is not a change in supply, just movement along the curve.

    • Important terminology: a change in demand induces a change in quantity supplied along the existing supply curve; it is not a change in supply.

  • Demand shock vs supply shock (symmetry):

    • Demand shock → shift the demand curve; price/quantity move to a new equilibrium with a new demand schedule.

    • Supply shock → shift the supply curve; price/quantity move to a new equilibrium with a new supply schedule.

    • Price itself is not the shock; shocks are exogenous and outside the model; price is inside the model and moves as a response.

  • Quick recap of the two curves and what changes when shocks occur:

    • Demand curve: shifts when non-price factors alter willingness to pay across all prices (i.e., new curve). Movement along the curve happens when price changes.

    • Supply curve: shifts when non-price factors alter willingness to supply at all prices. Movement along the curve happens when price changes.

  • Quick mental model for demand shocks (examples):

    • Higher preferences for a good → demand curve shifts right (higher quantity at every price).

    • Higher income for consumers → demand shifts right for normal goods (and left for inferior goods).

    • Prices of related goods: if substitutes become relatively more attractive, or a complementary good becomes cheaper, demand shifts accordingly.

  • Quick mental model for supply shocks (examples):

    • Technological improvement → supply curve shifts right (lower cost); more can be produced at each price.

    • Higher input costs → supply shifts left (less supply at each price).

    • Government actions: taxes can shift supply left; subsidies or stimulus can shift supply right.

    • Producer expectations: if producers expect higher future prices, they may hold back supply now, shifting supply left; if they expect prices to fall, they may shift supply right.

  • Graphical intuition for equilibrium with shocks:

    • If demand rises and supply is constant: equilibrium price and quantity rise (P↑, Q↑).

    • If demand falls and supply is constant: equilibrium price and quantity fall (P↓, Q↓).

    • If supply rises and demand is constant: price falls, quantity rises (P↓, Q↑).

    • If supply falls and demand is constant: price rises, quantity falls (P↑, Q↓).

    • If demand increases by the same amount as supply decreases (simultaneous shocks with opposite directions): price rises, quantity may remain unchanged (P↑, Q≈ unchanged).

    • If demand decreases by the same amount as supply increases: price falls, quantity may remain unchanged (P↓, Q≈ unchanged).

  • Movement vs shifts: comprehension checks (summary)

    • Movement factor (price) moves along an existing curve; shift factor (non-price) shifts the curve.

    • Demand shifters are non-price related (preferences, income, prices of related goods).

    • Supply shifters are non-price related (technology, input costs, regulations/taxes/subsidies, producer expectations).

  • First-order notes on the algebra and the standard linear model

    • Linear demand curve (in the common textbook form):
      Qd=a−bPQ_d = a - b P

    • Linear supply curve:
      Qs=c+dPQ_s = c + d P

    • Here: a, b, c, d are constants with b > 0 and d > 0. Price is the independent variable in Qd and Qs as written.

    • Equilibrium condition: set quantity demanded equal to quantity supplied: Q<em>d=Q</em>sQ<em>d = Q</em>s

    • Solve for equilibrium price P: a−bP</em>=c+dP∗⇒P∗=a−cb+da - b P^</em> = c + d P^* \Rightarrow P^* = \frac{a - c}{b + d}

    • Equilibrium quantity Q* (using either equation):
      Q∗=a−bP∗=c+dP∗=ad+bcb+dQ^* = a - b P^* = c + d P^* = \frac{ad + bc}{b + d}

    • In practice, some texts plot quantity as a function of price (Q as a function of P), which yields the inverted form of the demand curve. The interpretation is that quantity demanded responds to price; price is the variable that moves along the curve, not the other way around.

  • Shifts and the delta notation

    • A demand shock that raises the intercept by Δa changes the demand function to:
      Qd=(a+Δa)−bPQ_d = (a + \Delta a) - b P

    • New equilibrium price with the shifted demand curve:
      P′=(a+Δa)−cb+dP' = \frac{(a + \Delta a) - c}{b + d}

    • Change in price due to the demand shift (the delta of price):
      ΔP=P′−P∗=Δab+d\Delta P = P' - P^* = \frac{\Delta a}{b + d}

    • Change in equilibrium quantity due to the demand shift (the delta of quantity):
      ΔQ=Q<em>′−Q</em>=dΔab+d\Delta Q = Q^<em>' - Q^</em> = \frac{d \Delta a}{b + d}

    • A supply shock that raises the intercept (i.e., changes the supply intercept) by Δc changes the supply function to:
      Qs=(c+Δc)+dPQ_s = (c + \Delta c) + d P

    • New equilibrium price with the shifted supply curve:
      P′′=a−(c+Δc)b+dP'' = \frac{a - (c + \Delta c)}{b + d}

    • Change in price due to the supply shift:
      ΔP=P′′−P∗=−Δcb+d\Delta P = P'' - P^* = -\frac{\Delta c}{b + d}

    • Change in equilibrium quantity due to the supply shift:
      ΔQ=Q<em>′′−Q</em>=−dΔcb+d\Delta Q = Q^<em>'' - Q^</em> = -\frac{d \Delta c}{b + d}

  • Intuition about elasticity and slope

    • The slope m in the linear demand curve Q_d = a - b P is m = -b (negative, since demand slopes downward).

    • The slope of the supply curve Q_s = c + d P is m = +d (positive, since supply slopes upward).

    • The slope is related to elasticity: price elasticity of demand at a point is
      ε<em>d=dQ</em>ddP⋅PQ=(−b)⋅PQ.\varepsilon<em>d = \frac{dQ</em>d}{dP} \cdot \frac{P}{Q} = (-b) \cdot \frac{P}{Q}.

    • Elasticity tells how responsive quantity is to price changes; the slope alone does not tell the full story, but it is a key component of elasticity.

  • Practical exercise: translating graphs to algebra and vice versa

    • Start with a simple demand curve and a simple supply curve; identify the equilibrium price and quantity graphically, then solve the same using the linear equations.

    • Practice shifting one curve (e.g., increase in demand by Δa) and compute the new P* and Q* using the delta formulas above.

    • If a simultaneous shock occurs (e.g., demand increases by Δa and supply decreases by Δc), use the two shifted equations and solve the new system to obtain the new equilibrium.

  • Worked numerical example (to cement understanding)

    • Example parameters: let
      $a = 100$, $b = 2$, $c = 20$, $d = 3$.

    • Baseline equilibrium:
      P∗=a−cb+d=100−202+3=805=16.P^* = \frac{a - c}{b + d} = \frac{100 - 20}{2 + 3} = \frac{80}{5} = 16.
      Q∗=a−bP∗=100−2(16)=68.Q^* = a - b P^* = 100 - 2(16) = 68.

    • Demand shift with Δa = 10 (new demand intercept higher):
      P′=(a+Δa)−cb+d=110−205=905=18.P' = \frac{(a + \Delta a) - c}{b + d} = \frac{110 - 20}{5} = \frac{90}{5} = 18.
      Q′=(a+Δa)−bP′=110−2(18)=74.Q' = (a + \Delta a) - b P' = 110 - 2(18) = 74.

    • Thus: ΔP=P′−P∗=2,ΔQ=Q′−Q∗=6.\Delta P = P' - P^* = 2,\quad \Delta Q = Q' - Q^* = 6.

    • Also check with the other equation: Qs′=c+dP′=20+3(18)=74.Q_s' = c + d P' = 20 + 3(18) = 74.

    • Supply shift with Δc = -15 (supply intercept falls, i.e., supply shifts right):
      P′′=a−(c+Δc)b+d=100−(20−15)5=955=19.P'' = \frac{a - (c + \Delta c)}{b + d} = \frac{100 - (20 - 15)}{5} = \frac{95}{5} = 19.
      Q′′=c+Δc+dP′′=5+3(19)=62?Q'' = c + \Delta c + d P'' = 5 + 3(19) = 62?

    • Note: using the corrected substitution: Q'' via either curve gives consistent result; using Qd at P'': Q'' = a - b P'' = 100 - 2(19) = 62. Also Qs'' = (c + \Delta c) + d P'' = 5 + 3(19) = 62. So ΔP=19−16=+3,ΔQ=62−68=−6.\Delta P = 19 - 16 = +3, \Delta Q = 62 - 68 = -6.

    • This example demonstrates that a leftward shift in supply (or rightward shift, depending on sign convention) can raise price and reduce quantity.

  • Summary of key takeaways

    • Exogenous shocks are outside the model; they shift curves (demand or supply).

    • Movement along a curve is caused by price changes (movement factor); shifts are caused by non-price factors (shift factors).

    • The equilibrium price and quantity respond to shocks according to supply and demand curves and can be quantified with simple linear models.

    • Delta notation is used to describe how much the equilibrium changes: ΔP,ΔQ.\Delta P, \Delta Q.

    • Comparative statics is the study of before-and-after equilibria under shocks.

  • Quick preview to connect with later topics

    • We will use these graphs and delta results to transition into IS-LM-type frameworks and macroeconomic equations, where we translate stories into mathematical relationships and then solve for macro variables.

  • Final practical note

    • When practicing with graphs, draw both demand and supply curves and work intersection-by-intersection for each scenario. If you get an answer wrong, redraw and re-check shifts vs movements. The process reinforces understanding and prepares you for exams where you will be asked to identify equilibrium outcomes under various shocks.

  • Polished comprehension check (reiterated):

    • Price changes cause movement along curves; shocks cause shifts of curves.

    • A higher price does not by itself imply the demand curve shifted right; it could be a result of supply shifting left or a demand shift; the full answer depends on which curve shifted and by how much.

    • In the linear model, equilibrium is found by solving two linear equations; delta notation helps track how shocks propagate to price and quantity.

  • Note on terminology pitfalls

    • Some phrases in the lecture mix up demand vs quantity demanded; the correct reading is:

    • Price increases lead to a movement along the demand curve, reducing quantity demanded, not shifting the curve.

    • A change in demand means the entire curve shifts; a change in quantity demanded means movement along the same curve.

  • Ethical/real-world relevance

    • Understanding how exogenous shocks affect prices and quantities helps explain policy responses, market interventions, and how different sectors react to external events (e.g., technology advances, income changes, regulations).

  • Preview: next steps

    • We'll move from graphical intuition to algebraic equations, derive the formulas more systematically, and practice translating between stories and equations.