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

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

3. 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

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

5. 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

6. 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

7. 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

8. Own-Price Elasticity and Total Revenue
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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.

9. 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

10. 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

11. 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

12. 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