Econ 201 Essential Mathematical Tools Economics as a

Econ 201 Essential Mathematical Tools Economics as a Marginalist Paradigm

Marginal Costs – What do we mean by marginal costs? • incremental, or additional, costs of producing one more unit of output – Difference in total costs of producing one more unit – Marginal cost of the 4 th unit = Total Costs of the 4 th unit minus the Total Costs of the 3 rd unit MC[4] = TC[4] – TC[3]

A Numeric Example • From Alchian and Allen # Tees produced daily Total Costs 0 $1. 00 1 $1. 90 2 $2. 70 3 $3. 40 4 $4. 00 5 $4. 70 6 $5. 50 7 $6. 40 8 $7. 40 9 $8. 60 Marginal Costs

A Numeric Example • What Are the Marginal Costs # Tees produced daily Total Costs Marginal Costs 0 $1. 00 --- 1 $1. 90 $0. 90 2 $2. 70 $0. 80 3 $3. 40 $0. 70 4 $4. 00 $0. 60 5 $4. 70 $0. 70 6 $5. 50 $0. 80 7 $6. 40 $0. 90 8 $7. 40 $1. 00 9 $8. 60 $1. 20

All of the Numbers # tees/day Total Cost Marg Cost Total Rev Marg Rev Profit Marg Profit 0 $1. 00 $0. 00 -$1. 00 1 $1. 50 $0. 50 $1. 00 -$0. 50 2 $2. 70 $1. 20 $2. 00 $1. 00 -$0. 70 -$0. 20 3 $3. 40 $0. 70 $3. 00 $1. 00 -$0. 40 $0. 30 4 $4. 00 $0. 60 $4. 00 $1. 00 $0. 40 5 $4. 70 $0. 70 $5. 00 $1. 00 $0. 30 6 $5. 50 $0. 80 $6. 00 $1. 00 $0. 50 $0. 20 7 $6. 40 $0. 90 $7. 00 $1. 00 $0. 60 $0. 10 8 $7. 40 $1. 00 $8. 00 $1. 00 $0. 60 $0. 00 9 $8. 60 $1. 20 $9. 00 $1. 00 $0. 40 -$0. 20

What Do They Mean? Total and Marginal Costs Marginal and Total Costs increasing at Increasing rate Marginal Costs at Minimum, TC increasing at dec rate

What’s It Mean to a Supplier? • Firm’s supply decision – Supply up to the point where p >= MC • Profit maximizing point Profit Max MR = MC

From the Demand Side • First Law of Demand – What Does Law Of Demand Mean? – all other factors being equal, as the price of a good or service increases, consumer demand for the good will decrease and vice versa. • Investopedia explains Law Of Demand. . . – summarizes the effect price changes on consumer behavior. For example, a consumer will purchase more pizzas if the price of pizza falls. The opposite is true if the price of pizza increases. – http: //www. investopedia. com/terms/l/law ofdemand. asp

A Demand Example Price Qty Demanded $10. 00 1 $9. 00 2 $8. 00 3 $7. 00 4 $6. 00 5 $5. 00 6 $4. 00 7 $3. 00 8 $2. 00 9 $1. 00 10

Consumer’s Marginal Value • Some basic definitions – Total Willingness-to-pay: “value in use” • How much would you be willing to pay for x units of the good than go entirely without? – Equals the area under the demand curve up to x units WTP for 4 units

Computing Marginal Value Price Qty Demanded $10. 00 1 $9. 00 2 $8. 00 3 $7. 00 4 $6. 00 5 $5. 00 6 $4. 00 7 $3. 00 8 $2. 00 9 $1. 00 10

Total and Marginal Value Price Qty Demanded Amt Paid Marginal Value Total Value $10. 00 1 $10. 00 $9. 00 2 $18. 00 $9. 00 $19. 00 $8. 00 3 $24. 00 $8. 00 $27. 00 $7. 00 4 $28. 00 $7. 00 $34. 00 $6. 00 5 $30. 00 $6. 00 $40. 00 $5. 00 6 $30. 00 $5. 00 $4. 00 7 $28. 00 $49. 00 $3. 00 8 $24. 00 $3. 00 $52. 00 $2. 00 9 $18. 00 $2. 00 $54. 00 $1. 00 10 $10. 00 $1. 00 $55. 00 Price x Qty Dem Area under Demand Difference in TV(3)-TV(2) MV is also equal to price paid

In Graphic Terms Note: (again) price = marginal value Consumer is willing to buy up to P = MV

What Have We Learned? • How to compute marginal or incremental values – Marginal cost: the additional (change in Tot Costs) of producing one more unit – Marginal value: the value to a consumer of purchasing one more unit

The Bigger Lesson • Sell rule for firms – Firms will supply up to the point where the MC of producing the next unit are just equal to the price it receives for the good • First law of supply: supply curves will be upward sloping • Buy rule for consumers – Consumers will buy up to the point that price equals MV • First law of demand: demand curves are downward sloping • Negative slope diminishing marginal value of consuming next unit