CH2_Demand_supply - Intermediate Microeconomic Analysis...

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Unformatted text preview: Intermediate Microeconomic Analysis Demand, Supply and Market Equilibrium Instructor: Bin Xie Spring 2015 Demand Function The quantity of a good or service that consumers demand depends on price and other factors such as consumers' incomes and the prices of related goods. Demand Function: the mathematical relationship between quantity demanded (Qd ), price (p ) and other factors that inuence purchases (e.g. income Y ) Qd = D(p, ps , pc , Y ) p : price of the good or service ps : price of a substitute good pc : per unit price of a complementary Y : consumers' income good Demand Function (Cont.) Usually (in this course) the demand function takes a linear form. Example Qd = 210 − 20p + 20ps − 15pc + 3Y Qd : Quantity of pizza demanded p : price of pizza ps : price of hamburger pc : price of coke Y : your income Demand Function (Cont.) Graphically (two-dimension), only the relationship between Q and p is depicted, and other factors are held constant (ceteris paribus assumption) Example ps = 3; pc = 2; Y = 20 Qd = 210 − 20p + 20 × 3 − 15 × 2 + 3 × 20 = 300 − 20p The relationship between Qd and p can be shown by the movement along the demand curve. The relationship between Qd and other factors (ps , pc , Y ) can be illustrated by the shift of the demand curve. How about the partial derivative of Qd with respect to p ? Supply Function The quantity of a good or service that rms supply depends on price and other factors such as cost of inputs. Supply Function: the mathematical relationship between quantity supplied (Qs ), price (p ) and other factors such as the cost of inputs Qs = S(p, ph ) p : price of the good ph : cost of inputs or service Supply Function (Cont.) Usually the supply function takes a linear form. Example Qs = 140 + 20p − 20ph Qs : Quantity of pizza supplied p : price of pizza ph : price of cheese Supply Function (Cont.) Graphically, we only depict the relationship between Qs and p , and hold other factors constant (ceteris paribus assumption) Example ph = 2 Qs = 140 + 20p − 20 × 2 = 100 + 20p The relationship between Qs and p can be shown by the movement along the supply curve. The relationship between Qs and other factors (ph ) can be illustrated by the shift of the supply curve. Market Equilibrium The interaction between consumers' demand curve and rms' supply curve determines the market price and quantity of a good or service that is bought and sold. Price is the bridge connecting buyers and sellers in a market, signalling both sides how many to buy/sell. Price too high: excess supply will drive the price down; Price too low: excess demand will push the price up. Equilibrium price: demand will equal supply. Conclusion: when there is excess supply or excess demand, natural market forces will push the quantity and price to market equilibrium. Market Equilibrium (Cont.) Graphically, market equilibrium occurs where the demand and supply curves intersect. Mathematically, nd the price that equates the quantity demanded Qd and the quantity supplied Qs . Qd = Qs 300 − 20p = 100 + 20p p = 5. Shocking the Equilibrium (Comparative Statics) As a policy concern, often we need to study what will happen to the equilibrium when there is an external shock. Suppose that supply curve is aected by an exogenous variable a: Qs = S(p, a) Qd = D(p) p could implicit function of the suppy-shifter a: Qd = D(p(a)), Qs = S(p(a), a) Demand curve is the same: At the market equilibrium, price be written as an Implicit function A function dened by an implicit equation (Qd = Qs ), by associating one variable with the others. (Here are p and a.) Shocking the Equilibrium (Cont.) In equilibrium, it is always established that D(p(a)) = S(p(a), a) To study the eect of the shock a on the equilibrium status: a, using the chain rule : ∂S(p(a), a) dp ∂S(p(a), a) dD(p(a)) dp = + dp da ∂p da ∂a Total derivative with respect to Rearranging the term yields: ∂S dp ∂a = dD ∂S da − dp ∂p . (What does this derivative mean?) Example Demand function D = −3p + 40. Supply function with an external shock S = 5p − 3a. dp Find out the comparative statics . da Elasticities The elasticity indicates how responsive one variable is to a change of another variable. For instance, the price elasticity of demand measures: how sensitive the percentage change of the demand Qd is to percentage changes in the price of that good P . ε= dQ/Q dQ P percentage change in quantity = = percentage change in price dP/P dP Q Elasticities (Cont.) Example Qd = 300 − 20p What is the demand elasticity? On a linear demand curve, the demand elasticities are NOT constant. Elasticities (Cont.) Income elasticity of demand εIncome = dQ/Q percentage change in quantity demanded = percentage change in income dY /Y cross-price elasticity of demand εPrice = percentage change in quantity demanded = percentage change in price of another good dQ/Q dPo /Po elasticity of supply η= dQ/Q percentage change in quantity supplied = percentage change in price dP/P Eects of Tax Two Types of Sales Tax: Ad valorem Tax (Proportional) and Unit Tax Ad valorem Tax is more prevalent in reality. The eect of a sales tax on equilibrium price and quantity depends on elasticities of demand and supply. (Who gets hurt more?) The incidence of tax on consumers/rms is only determined by the (demand and supply) elasticities, no matter where the government collects the tax from. Eects of Tax (Cont.) Suppose the price at market equilibrium before tax is p , a unit tax τ is collected from the producers. Producers only receive p−τ if the market price is still But the market equilibrium will change (exogenous tax) New equilibrium: D(p(τ )) = S(p(τ ) − τ ) Implicit Function! p. shock: Eects of Tax (Cont.) How to solve implicit function? Usually total derivative/dierential. In this case only chain rule is needed. Derivative with respect to τ of both sides: dS d(p(τ ) − τ ) dS dp dD dp = = ( − 1) dp dτ dp dτ dp dτ Rearrange: dS dS p dp η dp dp Q = = = dS dD dS p dD p dτ η−ε − − dp dp dp Q dp Q Eects of Tax (Cont.) dS dp η dp τ= τ= τ dS dD dτ η−ε − dp dp dD − dp −ε dp Tax incidence on rms: τ − τ = τ τ= dS dD dτ η−ε − dp dp Tax incidence on consumers: Excercise: What if the tax is collected from consumers? (Hint: consumers have to pay p + τ when the market price is still p ). Example Demand function D = −3p + 40. Supply function with an external shock S = 5p . If the government collects a unit tax from producers τ = 2, what are the tax incidences on consumers and producers? ...
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