Price Discrimination and Consumer Surplus Debi Bosselman Heather Isenhart Erin Meredith Samantha McGlennen Project 1

Assumptions A fundamental assumption is when calculus is applied to economics, functions of interest can be approximated with A fundamental assumption is when calculus is applied to economics, functions of interest can be approximated with We are assuming only (price and quantity) and that economics is as rigid as calculus, which it is not. Many other variables are involved, but not considered here. We are assuming only (price and quantity) and that economics is as rigid as calculus, which it is not. Many other variables are involved, but not considered here.

Supply and Demand Debi Bosselman

Supply and Demand Equilibrium The equilibrium price,p*, and quantity, q*, occur when the quantity at which the price offered (demand) and the price asked (supply) are equal: p*= D(q)=S(q).

Approximation of Demand Function When we use a continuous function, we are implicitly assuming that the jumps in these functions are small enough so that the continuous functions approximate the discrete ones very closely.

Price Discrimination and Consumer Surplus Heather Isenhart

Business Goals Maximize revenue…… Maximize revenue…… How do they maximize revenue? How do they maximize revenue?

Perfect Price Discrimination hypothetical situation

Value to the Consumer n  D(q¡)  q¡ i = 1

Consumer Surplus  Value beyond the price paid

Producer Surplus; The Effect of the Elasticities of Supply and Demand Erin Meredith

Producer Surplus The area below p = p* and above the supply curve. The integral below is used to find the producer surplus. The area below p = p* and above the supply curve. The integral below is used to find the producer surplus.

Linear Supply and Demand Curves These curves can be approximated by the following linear functions: These curves can be approximated by the following linear functions: D(q) = A – Bq D(q) = A – Bq S(q) = Cq S(q) = Cq A, B, C are positive constants A, B, C are positive constants

Elasticity of Demand The elasticity of demand for D(q) is the quantity (1/B)(p/q). The elasticity of demand for D(q) is the quantity (1/B)(p/q). A smaller B means that small changes in the price give a large change in the quantity demanded. The demand is highly elastic. A smaller B means that small changes in the price give a large change in the quantity demanded. The demand is highly elastic. When the demand has a small elasticity, or is inelastic, B is large, a large change in prices means a small change in demand. When the demand has a small elasticity, or is inelastic, B is large, a large change in prices means a small change in demand.

Elasticity of Supply The elasticity of supply for S(q) is the quantity (1/C)(p/q). The elasticity of supply for S(q) is the quantity (1/C)(p/q). If elastic, a small change in price means a large change in the quantity supplied. If elastic, a small change in price means a large change in the quantity supplied. If inelastic, a large change in price means a small change in supply. If inelastic, a large change in price means a small change in supply.

Problem: Comparing Elasticities of Supply and Demand C.S./P.S.= B/C = Elasticity of Supply/Elasticity of Demand C.S./P.S.= B/C = Elasticity of Supply/Elasticity of Demand The larger this proportion, the greater the surplus. The larger this proportion, the greater the surplus. This happens if producers are more sensitive to price changes than the consumers are. This happens if producers are more sensitive to price changes than the consumers are.

Two-Tier Price Discrimination and Maximum Revenue Samantha McGlennen

Two-Tier Price Discrimination A seller charges two prices A seller charges two prices –The higher price, p ¹ –The competitive price, p* Total Revenue = p ¹  q ¹ + p*(q*- q ¹ ) Total Revenue = p ¹  q ¹ + p*(q*- q ¹ )

Problem: Choosing p ¹ to maximize revenue The revenue function, f(q), is (p ¹  q ¹ ) + p*(q*- q ¹ ) The critical point for f(q) can be used to find p ¹ = D(q ¹ )

How do our assumptions affect our conclusions? This model works well for companies that deal in very large quantities of supply and demand, such as Wal-Mart. This model works well for companies that deal in very large quantities of supply and demand, such as Wal-Mart. However, this model would not work for smaller companies, such as Oley’s Pizza. However, this model would not work for smaller companies, such as Oley’s Pizza.