Dominick Salvatore Schaums Outline of Microeconomics, 4th edition Schaums Outline Series 2006

28 DEMAND, SUPPLY, AND EQUILIBRIUM: AN OVERVIEW [CHAP. 2
SUPPLY
2.11 (a) Express in simple mathematical language the discussion in Section 2.5.
(b) How do we arrive at the single producer’s supply schedule and supply curve for the commodity?
What do these show?
(a) What was said in Section 2.5 can be expressed in simple mathematical language as follows:
Qs x ¼ f(P x , Tech, P i , F n ) or Qs x ¼ f(P x ) cet: par:
where
Qs x ¼ the quantity supplied of commodity X by the single producer, over the specified time period
f ¼ a function of or depends on (the different symbol, i.e., f rather than f, signifies that we expect
a different specific functional relationship for Qs x from that of Qd x )
Tech ¼ technology
P i ¼ the price of inputs
F n ¼ features of nature such as climate and weather conditions. The bar on top of last three factors
indicates that they are kept constant (the cet. par. condition).
(b)
The second general mathematical expression reads: The quantity of commodity X supplied by a producer over
a specified time period is a function of or depends on the price of that commodity while certain other factors
remain constant.
Qs x ¼ f(P x ) cet: par: is a general functional relationship. In order to derive the single producer’s supply
schedule and supply curve, we must get that person’s specific supply function. The single producer’s supply
schedule and supply curve of a commodity show the alternative quantities of the commodity that the producer
is willing to sell over a specified period of time at various alternative prices for commodity X, while keeping
everything else constant. They show alternatives as seen by the producer at a particular point in time.
2.12 From the specific supply function Qs x ¼ 20P x (P x is given in dollars), derive (a) the producer’s supply
schedule and (b) the producer’s supply curve. (c) What things have been kept constant in the given
supply function? (d) What is the minimum price that this producer must be offered in order to
induce him or her to start supplying commodity X to the market?
(a) Table 2.14
P x ($) 6 5 4 3 2 1 0
QS x 120 100 80 60 40 20 0
(b)
The shape and location of a producer’s supply curve (if it exists) depend on production and cost conditions
(Chapters 6 and 8) and on the type of market organization in which the producer is operating (Chapters 9
to 12). From now on and unless otherwise specified, the supply curve will be taken to be positively sloped
(its usual shape).
Fig. 2-15