Inverse Supply
Inverse supply is a function which shows for each unit the minimum price at which that unit will be supplied.
While supply is a function from
$$
\text{ price } \rightarrow \text{ quantity supplied}
$$
inverse supply is a function from
$$
\text{ quantity supplied} \rightarrow \text{ price }
$$
Inverse supply: Graphical Illustration
Marginal Cost (MC)
Definition (Individual Firm's MC ): An individual firm's marginal cost for any given unit of a product or service, is the additional cost incurred by the firm for producing that additional unit.
Inverse supply and Marginal cost
If we assume that firms are interested in maximizing profit, which we do, then for any given unit of output, the minimum price at which the firm would be willing to and wants to sell the unit equals the marginal cost of that unit. Why?
Hence, the vertical height of the supply curve at any unit is the same as the firm's marginal cost of that unit.
Inverse supply and MC: Graphical Illustration
Meaning of Cost in Economics
In economics, we use the term cost to refer to both explicit as well as implicit costs.
Explicit costs refer to the payment made to others for resources owned by them.
Implicit costs refer to the opportunity cost of self-employed resources - the value of resources in their next best alternative use.
So when we speak of the additional cost of producing an additional unit, we are referring to both the additional explicit as well as implicit costs of producing that unit.
Exercise
Suppose the marginal cost of a firm for any given unit of output \( q \) is given by: $$ MC(q) = 10 + 2q \text{ for } q \geq 1. $$
Given what you know about the relationship of the supply curve and the MC curve, find the equation of the supply curve.
Relationship between the Supply curve and the MC: Importance
Knowing
(1) the relationship between MC and supply, and
(2) the meaning of cost in economics
will be helpful in understanding which factors change supply and how they change it.
Producer Surplus (PS)
Producer surplus on any unit of a product is the difference in the price at which that unit is sold and the marginal cost of that unit.
PS of a unit = (Price of that unit) - (MC of that unit)
Adding producer surplus across all units produced by a producer gives the total producer surplus enjoyed by the producer.
Adding producer surplus across all units consumed in a market gives the total producer surplus in the market.
Calculation of producer surplus (PS)
When calculating total PS across given units we can use two methods:
Method 1: Calculate producer surplus (PS) for each unit (using the definition on previous slide) and add the PS across different units.
Method 2: Calculate PS as the area below the price and above the supply curve (MC curve) for the given range of units.
Example of Method 1
Calculate producer surplus when wage = $13 per hour.
\begin{equation} PS = (13 - 7) + (13 - 9) + (13 - 11) = $12. \nonumber \end{equation}
Example of Method 2: PS as an area
Calculate producer surplus when wage = $13 per hour.
$$ PS = \frac{1}{2} \times (13 - 5) \times 4 = $32. $$
Should I use Method 1 or Method 2?
Depends on the data and the problem. If you have discrete data, such as in a table then you have to use Method 1.
If you have continuous data, such as a graph of the MC curve, or the supply curve, or their functional forms then use Method 2.
Even when you have continuous data, if you want to calculate PS for some specific, non-consecutive units then use Method 1.
In short, use method 1 when method 2 cannot really be used; otherwise, use Method 2.