Quantitative Demand Analysis Managerial Economics Kyle J. Anderson Kelley School of Business Indiana University

Revenue, Elasticity, and Monopoly Pricing Total revenue and marginal revenue Calculating marginal revenue Elasticity and marginal revenue Monopoly pricing decisions Kelley School of Business

Total Revenue Demand: Q = 50 – ½ P Inv. Demand: P = 100 – 2Q $ Revenue = Q*P Revenue = Q*(100 – 2Q) Revenue Max Marginal Revenue: Change in revenue due to a change in Q. Increasing Decreasing Q=50 (P=0) Q=0 Q Kelley School of Business

Marginal Revenue – linear demand P = 100 – 2Q TR = Q*P = Q*(100-2Q) TR = 100Q – 2Q2 MR = 100 - 4Q 100 – 4Q = 0 4Q = 100 Revenue max is where MR=0. (Q=25, P=50) If MC=0, then this is also profit maximizing.

Demand and Marginal Revenue 3-5 Demand and Marginal Revenue For a linear inverse demand function, MR has same intercept and twice the slope. P = 100 – 2Q MR = 100 – 4Q P 100 80 60 40 20 Q 10 20 40 50 MR

Maximizing profits Profit maximizing occurs where MR=MC. 3-6 Maximizing profits Profit maximizing occurs where MR=MC. Assume MC=$20. P = 100 – 2Q MR = 100 – 4Q MR=MC 100 – 4Q = 20 Q = 20 P = 60 P 100 P* MC Q* Q 50 MR

Elasticity, Revenue and Linear Demand Would you rather have elastic or inelastic demand? P TR 100 Unit elastic Elastic Unit elastic High Output Lower Output Inelastic Q 10 20 30 40 50 Q 10 20 30 40 50 MR Elastic P = 100 – 2Q Inelastic TR = P*Q

Own-Price Elasticity and Total Revenue 3-8 Own-Price Elasticity and Total Revenue Elastic An increase in price leads to a decrease in total revenue. Inelastic Increase in price leads to an increase in total revenue. Unitary Total revenue is maximized at the point where demand is unitary elastic.

Monopoly profits Profit maximizing occurs where MR=MC. 3-9 Monopoly profits Profit maximizing occurs where MR=MC. If MC=0, profit max is where e = -1 If MC>0, profit max is on elastic portion of demand. P 100 Elastic Unit elastic P* Inelastic MC Q* Q 50 MR

Monopoly profits Maximize marginal profits. Some consumer surplus. 3-10 Monopoly profits Maximize marginal profits. Some consumer surplus. Deadweight Loss – inefficiency due to reduced output and higher price. P 100 Consumer Surplus Marginal Profits P* Deadweight Loss MC Q* Q 50 MR

What we’ve learned: Firms profit maximize by setting MR=MC. How to calculate marginal revenue. Revenue is maximized where ε = -1. Profits are maximized on the elastic portion of the demand curve (except when MC=0). Profit maximization by monopolies leads to positive marginal profits, some consumer surplus, and some inefficiency (deadweight loss). Kelley School of Business

Putting elasticity to use You can use regression analysis to estimate the elasticity of demand for their products. Simple rules – if I raise price by 5% and quantity demanded falls by 3%, what does this mean? Kelley School of Business