Introduction
The willingness and ability to sell a good or service is called supply. In general, producers are willing to sell their product for a price as long as that price is at least as high as the cost to produce an additional unit of the product. It follows that the willingness to supply, called the supply function, depends on the price at which the good can be sold as well as the cost of production for an additional unit of the good. The greater the difference between those two values, the greater is the willingness of producers to supply the good.
In subsequent chapters, we will explore the cost of production in greater detail. At this point, we need to understand only the basics of cost. At its simplest level, production of a good consists of transforming inputs, or factors of production (such as land, labor, capital, and materials), into finished goods and services. Economists refer to the rules that govern this transformation as the technology of production. Because producers have to purchase inputs in factor markets, the cost of production depends on both the technology and the price of those factors. Clearly, willingness to supply is dependent on not only the price of a producer’s output, but additionally on the prices (i.e., costs) of the inputs necessary to produce it.
For simplicity, we can assume that the only input in a production process is labor that must be purchased in the labor market. The price of an hour of labor is the wage rate, or W. Hence, we can say that (for any given level of technology) the willingness to supply a good depends on the price of that good and the wage rate. This concept is captured in Equation 1-7, which represents an individual seller’s supply function:
where Qs x is the quantity supplied of some good X (such as gasoline), Px is the price per unit of good X, and W is the wage rate of labor in, say, dollars per hour. It would be read, “The quantity supplied of good X depends on (is a function of) the price of X (its own price), the wage rate paid to labor, and so on.” Just as with the demand function, we can consider a simple hypothetical example of a seller’s supply function. As mentioned earlier, economists often will simplify their analysis by using linear functions, although that is not to say that all demand and supply functions are necessarily linear. One hypothetical example of an individual seller’s supply function for gasoline is given in Equation 1-8:
Notice that this supply function says that for every increase in price of $1, this seller would be willing to supply an additional 250 units of the good. Additionally, for every $1 increase in wage rate that it must pay its laborers, this seller would experience an increase in marginal cost and would be willing to supply five fewer units of the good. We might be interested in the relationship between only two of these variables, price and quantity supplied. Just as we did in the case of the demand function, we use the assumption of ceteris paribus and hold everything except own-price and quantity constant. In our example, we accomplish this by setting W to some value, say, $15. The result is Equation 1-9:
in which only the two variables Qs x and Px appear. Once again, we can solve this equation for Px in terms of Qs x , which yields the inverse supply function in Equation 1-10:
The graph of the inverse supply function is called the supply curve, and it shows simultaneously the highest quantity willingly supplied at each price and the lowest price willingly accepted for each quantity. For example, if the price of gasoline were $3 per gallon, Equation 1-9 implies that this seller would be willing to sell 500 gallons per week. Alternatively, the lowest price the seller would accept and still be willing to sell 500 gallons per week would be $3. Exhibit 1-3 represents our hypothetical example of an individual seller’s supply curve of gasoline. What does our supply function tell us will happen if the retail price of gasoline rises by $1? We insert the new higher price of $4 into Equation 1-8 and find that quantity supplied would rise to 750 gallons per week. The increase in price has enticed the seller to supply a greater quantity of gasoline per week than at the lower price.
Related Links:
DEMAND AND SUPPLY ANALYSIS: INTRODUCTION
Demand Function and the Demand Curve
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