Lecture 3

# Lecture 3 - 4/9/2007 Outline of Next 3 Classes Recap of...

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4/9/2007 1 Outline of Next 3 Classes • Recap of optimal pricing • What does the demand curve for your product look like? • Advanced pricing – Price discrimination – Bundling – Intertemporal pricing (e.g. learning by doing) Optimal Pricing - I • Simple model: – Can only charge single price – No competitors/substitutes that respond to your pricing – Demand and Costs constant over time Demand and Costs constant over time • Numeric example: Demand: Q = 100 - P Costs: MC = AC = 10 What decision maximizes profits for this firm? Optimal Pricing - II • Aside: What is this firm deciding on? –A) Q – B) P – C) both Q and P – D) either Q or P

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4/9/2007 2 Optimal Pricing - III • Let’s think of firm deciding on Q • Write profit as a function of Q: Π = TR – TC = P · Q – MC·Q = (100-Q) · Q – 10Q = 90Q - Q 2 • To maximize profits , set d Π/ dQ =0 d Π/ dQ = 90 – 2Q = 0 Q = 45 (note: d Π/ dQ = MR – MC) Optimal Pricing – IV • And the profit maximizing price is P = 100 - Q = 55 • Note: Alternatively, we could have considered the firms decision of P, i.e. 1) written profits as a function of P, 2) set d Π/ dP =0, 3) found optimal P, and then 4) used the demand curve to compute optimal Q. • This method would give us the exact same result (P=55,Q=45) Optimal Price and Quantity 80 100 120 MR=MC 0 20 40 60 0 20 40 60 80 100 120 Quantity Price Demand MR MC=AC P c Q c 55 45
4/9/2007 3 More General Derivation • Profit: Π (Q) = TR – TC =P(Q)·Q–TC(Q) • To maximize , set d Π/ dQ =0 Π dQ = dP dQ Q+P MC(Q) = d Π/ dQ = dP / dQ · Q + P – MC(Q) = 0 – P · dP / dQ · Q/P = P – MC(Q) (P – MC(Q))/P = -1/ η • In words, the percentage markup is equal to –1 over the price elasticity of demand. • So: The less negative the demand elasticity is (the less elastic is demand), the higher the markup (and profit) is. What does the Demand Curve for your Product Look Like? • The above assumes that you know what the demand curve looks like. Unfortunately, this is typically not the case, particularly for new products. • Estimating demand for your product. – 1) Market Experimentation – 2) Use Historical Data – 3) Consumer Surveys Market Experimentation - I • Basic Idea: Purposely set different prices in N different markets. Use (P i ,Q i ) data points to “estimate” the demand curve estimate the demand curve. • e.g. – Set different prices in different time periods.

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## This note was uploaded on 09/03/2009 for the course ECON 106E taught by Professor Ackerberg during the Spring '08 term at UCLA.

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Lecture 3 - 4/9/2007 Outline of Next 3 Classes Recap of...

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