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Tutorial 3: Demand and Supply (cont.)

 

Market Supply

In Tutorial 2 we learned that the minimum price a seller is willing to accept in exchange for one unit of a good or service is called her reservation price. Seller reservation prices vary, in part, due to differences in the costs of production. Some firms may be subsidized or taxed, face different prices for inputs, have different expectations regarding how demand for their product will change, or use different production technology.

This indicates that the quantity of a good supplied by sellers varies with market price, all these other influences held constant. As market price rises, more sellers will have a reservation price low enough to make the sale worthwhile. That's because as price rises, producers can afford to employ more inputs and offer more of the good for sale. As price falls, fewer sellers will have a reservation price low enough to make the sale worthwhile. That's because as price falls, producers cannot afford to employ as many inputs and thus offer fewer units of the good for sale.

We can use mathematics notation to write a shorthand expression of this relationship as:

QS = f (Price | SP-PENT),

where

QS =

Quantity of the good supplied in this market during a given time period

 

Price =

The market price of the good

 

| =

"given" or "holding these variables constant"

 

S =

Subsidies (or taxes) levied on sellers

 

Pi =

Price of factor inputs used to produce the good

 

Ps =

Price of substitutes in production

 

E =

Expectations sellers have of future changes in the demand for their product

 

N =

Number of sellers in this market

 

T =

Level of Technology used in production of the good

 

A linear equation describing market supply for a good might be written as:

QS(P, SPPENT) = c + d1*Price + d2*Sub - d3*Tax - d4*Pi - d5*Ps - d6*E(Price) + d7*N + d8*T

The sign of the intercept term, c, could be positive, zero, or negative. This indicates that if all the variables were set to zero, the seller may offer a positive amount of the good, no amount of the good, or a negative amount of the good for sale. (In the latter case, a positive price would be required before any quantity was offered for sale.)

The sign on coefficients d1, d2, d7, and d8 are all positive. This indicates that an increase in the value of any one of these variables (price, subsidies, number of sellers, or technology) will increase the quantity supplied, ceteris paribus.

The sign on coefficients d3, d4, d5, and d6 are all negative. This indicates that an increase in the value of any one of these variables (taxes, the price of inputs, the price of substitutes in production, or expectation of a drop in consumer demand) will decrease the quantity supplied, ceteris paribus.

If we hold the variables SP-PENT constant and only allow the independent variable Price to vary, we can write the equation for market supply as:

QS(Price | SP-PENT) = d0 + d1*Price,

where d0 = d2*Sub - d3*Tax - d4*Pi - d5*Ps - d6*E(Price) + d7*N + d8*T.

Let d0 = 0 and d1 = 2. The resulting supply equation is

QS(P) = 0 + 2*P.

The inverse form of this equation1 is depicted graphically as an upward-sloping line in Price/Quantity space:

Graph of inverse supply equation.

 

This supply curve (S1) depicts the minimum Price of a good sellers are willing to accept (in $ per unit) to offer a given Quantity for sale during a specified period of time (units/t), everything else (e.g., SP-PENT) held constant.

 

Now it's time to "do the thing".

Click on the following link to download the Demand and Supply Workbook. Work through Warmup Questions 6 - 11 to improve your understanding of how changes in SP-PENT shift the supply curve.

Return here when you have finished.

(Need help downloading the Excel file?)

 

Now we turn our attention to how the interaction between buyers and sellers in the context of a market determines the equilibrium market price and quantity...


1 Starting from our original equation, the equation for the inverse supply curve is given by P(QS | SPPENT) = -(d0/d1) + (1/d1)*QS. [return to text]