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 4th unit = Total Costs of the 4th unit minus the Total Costs of the 3rd unit MC[4] = TC[4] – TC[3]

A Numeric Example From Alchian and Allen # Tees produced daily Total Costs Marginal Costs $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

A Numeric Example What Are the Marginal Costs # Tees produced daily Total Costs Marginal Costs $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 6 $5.50 7 $6.40 8 $7.40 9 $8.60 $1.20

All of the Numbers # tees/day Total Cost Marg Cost Total Rev Marg Rev Profit Marg Profit $1.00 $0.00 -$1.00 1 $1.50 $0.50 -$0.50 2 $2.70 $1.20 $2.00 -$0.70 -$0.20 3 $3.40 $0.70 $3.00 -$0.40 $0.30 4 $4.00 $0.60 $0.40 5 $4.70 $5.00 6 $5.50 $0.80 $6.00 $0.20 7 $6.40 $0.90 $7.00 $0.10 8 $7.40 $8.00 9 $8.60 $9.00

What Do They Mean? Total and Marginal Costs Marginal and Total Costs increasing at Increasing rate Total and Marginal Costs 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/lawofdemand.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 $9.00 2 $18.00 $19.00 $8.00 3 $24.00 $27.00 $7.00 4 $28.00 $34.00 $6.00 5 $30.00 $40.00 $5.00 6 $45.00 $4.00 7 $49.00 $3.00 8 $52.00 $2.00 9 $54.00 $1.00 10 $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 Buy rule for consumers 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