Supply function of a firm or of a group of firms (industry) relates the quantity of a commodity that the seller (s) is willing and able to supply to the factors that determine the supply. The foregoing production and cost analyses and the discussion on the objectives of the firm have thrown enough light on the determinants of supply. The important one are:
(a)Product price (Px)
(b) Factor productivities (efficiencies) or the state of technology (FE)
(c) Factor prices (FP)
(d) Prices of other products related in production(PR)
(e) Firmâ€™s goals (G)
(f) Weather, strikes and such other short run forces (W)
(g) Firmsâ€™ expectations about future prospects for prices, costs, sales and the state of the economy in general (E).
(h) Number (N) and character of the firm ( C ) in the industry
Putting all these factors together, the supply function can be written as
Sx = f (Px, FE, FP, PR, G, W, E, N, C)
Supply of a good varies directly with its own price, other things remaining the same. This is called the law of supply, which together with the law of demand, constitutes the most important laws in economics. Its rationale lies in the law of diminishing returns. Translated into cost terms, the law of diminishing returns means that the addition to total costs f producing a unit of the good rises as total output expands. Further, if cost rises as output expands; a firm would produce and supply more of a good only if it could command a higher price for its product. Thus, as price goes up, ceteris paribus supply goes up, and vice versa.
The upward sloping market supply curve could also be explained through incentive for new firms to enter the industry. When the prices go up, other things remaining the same, profitability is increased, which in turn attracts the new firms to the industry. Since the number of firms influences the aggregate supply the entry of new firms would tend to increase the market supply. Thus, supply varies directly with the price because the higher the price, the stronger is the incentive for existing firms to expand their output and for new firms to move on to the production of the product whose price has risen.
As explained above, the higher the factor productivities, the lesser the input requirements and lesser is the total cost of production for a given level of output. Further, a reduction in total cost of production lowers the cost of production lowers the cost curves, including the marginal cost curve, which, through the supply curve analysis of the previous section, leads to an increase in supply. Thus, increase in factor productivities. Ceteris paribus brings an increase in supply, and vice versa. Incidentally note that since there are more than one factors of production, factor productivities is a set of variable rather than just one variable. Increase in factor prices, ceteris paribus, leads to increase in production cost, which, in turn, induces the firm to restrict their supply. Thus, factor prices exercise a negative impact on supply. Like factor productivities, factor prices constitute a vector of variables. Just as prices of goods related in consumption exert influence on consumers demand for goods and services, prices of goods related in production influence the firmsâ€™ supply of goods and services. Thus, for example, an increase in the price of the color television ceteris paribus, would lead to a decrease in the supply of black and white television (BWTV) and vice versa. This is because, CTV and BWTV are substitutes in production-that is, the firm could choose the composition of the two types of televisions in the direction indicated above. Quite the opposite would have happen in the face of a change in the price of an item which is complementary in production. For instance, if the price of milk goes up, other things remaining the same, the supply of butter would increase, and vice versa. This happens because milk price have increased and the dairies induced to go for expansion, to increase milk supply since increased supply of butter would increase as well. Once again, since it is conceivable that a product has more than one related good in production, the price of related goods variable is a vector of variables instead of a single one.
The objective or goal of the firm would also have a bearing on the supply. For instance, the firm whose objective is maximum sales, in general, would supply more than the one whose objective was maximum profit, other things remaining the same. It is obvious that short term factors such as weather, strikes, lockouts, have short term impact on supply of goods and services. For example, supply of woolen garments tends to increase in summer, as there are few buyers and there is a carrying cost of inventories. Strikes and lockouts have depressing effects on supplies.
Like consumers expectations influence their demands, sellers expectations have bearings on their supplies. If sellers expect that their product is going to be in short supply at a later that they can charge high prices, they would restrict their current supplies. If sellers expect that their product is going to be in short supply at a later date and that they can charge high prices, they would restrict their current supplies. Quite the reverse would happen if they fear a glut for their product. Similarly, sellersâ€™ expectations about future production costs vis-Ã -vis current production cost would influence their current supplies. For instance, if the shortage of raw-material is feared, supplies would decline and vice versa.
The number of sellers obviously has a positive impact on the aggregate supply of a good in the market. The character of sellers, in terms of their strategies of competition in the market, also has a bearing on aggregate supply. If sellers act like rivals, they would enter into cut throat competition and supply more of their products than otherwise. In contrast, if they collude, formally or otherwise, they would tend to restrict the supply of their product.
This would involve discussion of changes in supply and supply elasticity and demand analysis of supply function. The approach would be the same as adopted for demand analysis above, and the learning would be limited. For these reasons, no detail discussion on supply analysis is attempted here. Suffice it to point out, supply of a good expands and contrasts due to increase and decreases in that goods price, supply increase and decrease due to changes in any one or more of non-own price determinants of supply, and that there are a number of supply elasticity, one with respect to each of the supply determinants.