Question

List multiple (up to ten) economic functions across producer and consumer theory. Show what they are a function of. An example would be the production function; listed it as q = f(K,L) where K is capital and L is labor. Other functions may include the utility function, the demand function, the supply function, elasticities, etc.

Answer 1

Solution:

Around 10 economic functions across consumer and producer theory are:

1) Production function: q = f(K, L), q is output which is function of inputs capital, K and labor, L.

2) Cost function: C = g(q), C is the total cost, which is function of output.

(From total cost, many more functions such as average cost, marginal cost, etc. can be generated)

3) Revenue function: R = h(p, Q), R is the revenue earned by firm, which is function of price, p and quantity demanded, Q.

4) Demand function: Q = j(p), Q is the quantity demanded at price, p, so demand function is a function of price.

5) Using this, an inverse demand function can also be formed, which involves modification of the above equation and writing price, p as a function of quantity demanded, Q. So, inverse demand function: p = k(Q)

6) From above functions, profit function can also be formed. Substituting the inverse demand function in revenue function (that is substituting p = k(Q) in R), gives revenue as a function of quantity only. Using cost and revenue function, profit function can be generated. Furthermore, since both cost and revenue functions are functions of quantity, profit will also be function of quantity (assuming no inventory or wastage)

So, P = m(Q), So, profit, P, as function of quantity, Q (= q)

7) Similar to demand function, we can also derive supply function. Here also, quantity supplied will be function of price, p. The only major difference between supply and demand functions are that supply functions are from firm's viewpoint, and thus here Q and p are positively related as with increase in price of a good, firms would like to supply more of it, while demand functions are from consumer's viewpoint, and thus here Q and p are negatively related as with increase in price of a good, consumers would like to demand and consume less of it.

So, Qs = n(p), Qs is quantity supplied, which is function of price, p.

8) Now, that we have stepped on to the consumer theory part of economics, we should surely talk about utility functions. Utility function is one of the most important functions in consumer theory, as it indicates the satisfaction of a consumer. Mainly, for simplest models, utility functions are written as function of two goods, to see how a consumer prefers the two goods, or what combination of the two, or how he chooses among those two goods (of course generalization of more than two goods can be made).

U = s(X, Y), U is the utility function, X and Y are the two goods in question.

9) To buy goods, a consumer has to spend some income. So, here we define the expenditure function:

E = v(p, m), E is the expenditure, which is function of prices (here p is the price vector of order n for say n goods (generalization)) and income, m.

10) Price elasticity of demand (supply) simply tells the degree of responsiveness of demand (supply) to change in prices.

So, it is percentage change in quantity divided by percentage change in prices. Since using a demand function (supply function) one can always substitute for a function of price, and the general form we get for elasticity is thus, as a function of price, since with change in price, demand (supply) changes, and that indicates elasticity.

e = w(p), e is elasticity which is function of price, p.