The inverse relationship between price of the commodity and quantity demanded for that commodity is because of the following reasons:
(i) Income effect:
(a) Quantity demanded of a commodity changes due to change in purchasing power (real income), caused by change in price of a commodity is called Income Effect.
(b) Any change in the price of a commodity affects the purchasing power or real income of the consumers although his money income remains the same.
(c) Whenpriceofa commodity rise more has to be spent on purchase of the same quantity of that commodity. Thus, rise in price of commodity leads to fall in real income, which will thereby reduce quantity demanded is known as Income effect.
(ii) Substitution effect:
(a) It refers to substitution of one commodity in place of another commodity when it becomes relatively cheaper.
(b) A rise in price of the commodity let coke, also means that price of its substitute, let Pepsi, has fallen in relation to that of coke, even though the price of Pepsi remains unchanged. So, people will buy more of Pepsi and less of coke when price of coke rises.
(c) In other words, consumers will substitute Pepsi for coke. This is called Substitution effect.
Price effect = Income effect + Substitution effect
(iii) Law of Diminishing Marginal Utility:
(a) This law states that when a consumer consumes more and more units of a commodity, every additional unit of a commodity gives lesser and lesser satisfaction and marginal utility decreases.
(b) The consumer consumes a commodity till marginal utility (benefit)he gets equals to the price (cost)they pay, i.e., where benefit = cost.
(c) For example, a thirsty man gets the maximum satisfaction (utility)from the first glass of water. Lesser utility from the 2nd glass of water, still lesser from the 3rd glass of water and so on. Clearly, if a consumer wants to buy more units of the commodity,he would like to do so at a lower price. Since, the utility derived from additional unit is lower.
(iv) Additional consumer:
(a) When price of a commodity falls, two effects are quite possible:
1. New consumers, that is, consumers that were not able to afford a commodity previously, starts demanding it at a lower price.
2. Old consumers of the commodity starts demanding more of the same commodity by spending the same amount of money.
(b) As the result of old and new buyers push up the demand for a commodity when price falls.

(i) A good is called 'inferior goods' when its demand falls with a rise in the income of a consumer and vice- versa.
(ii) For example, Jowar or Bajra for a poor person.
(iii) A good is inferior in a relative terms. It means, a good is inferior or normal is determined by the income level of a consumer.
(iv) When a consumer moves to higher income, he/she may consider some goods below their income status, and treats them as inferior.

(i) Law of demand is only an qualitative, and not a quantitative statement.
(ii) It indicates only the direction in which the quantity demanded will change with a change in price. It says nothing about the magnitude of such a change.
(iii) For example, price of coke rises from Rs.8 to Rs.10 per bottle, then as per law of demand, we can say that the demand for coke will fall. But the law does not give the actual amount by which the demand for coke will decline.

(i) It states that price of the commodity and quantity demanded are inversely related to each other, when other factors remain constant. It means, quantity demanded of the commodity rises due to fall in price of the commodity and vice-versa.
(ii) Ceteris Paribus means:
(a) Price of Related commodity remains constant.
(b) Income of a consumer remains constant.
(c) Taste and preferences of a household remains constant.

(iii)The law of demand makes a qualitative statement only and not quantitative. It indicates the direction of change in the amount demanded and it does not indicate the magnitude of change.
(iv) Law of demand is one sided. It explains only the effect of change in price on the quantity demanded. It states nothing about the effect of change in quantity demanded on the price of the commodity.

No, fall in income does not have the same effect on demand for the given commodity.
(i) If the given commodity is a normal good, the fall in income will reduce the demand for the normal goods.
(ii) If the given commodity is an inferior good, the fall in income will raise the demand for the inferior goods.
(iii) If the given commodity is a necessity, the fall in income will not change the demand for the necessity of goods.

(i) Complementary goods are those which are useless in the absence of other goods and which are demanded jointly.

(ii) There would always exist an inverse relationship between price of complementary goods and demand for given commodity.
(iii) It means, with a rise in price of complementary goods, the demand for given commodity falls and vice-versa.
(iv) For example pen and refill, tea and sugar are complements to each other.

(i) Substitute goods are those goods which can be used in place of another goods and give the same satisfaction to a consumer.

(ii) There would always exist a direct relationship between the price of substitute goods and demand for given commodity.
(iii) It means with an increase in price of substitute goods, the demand for given commodity also rises and vice-versa.
(iv) For example, Pepsi and Coke, tea and coffee are substitute to each other.

It can be seen from the given demand functions, that 20 consumers do not want to demand the goods at any price greater than or equal to Rs.\(\frac { 10 }{ 3 } \). All of them demand only at a price of less than Rs.\(\frac { 10 }{ 3 } \). 
For a single consumer d[P] = 10 - 3P For 20 consumers, d _market[P] = [10 x 3P] x 20 = 20 - 60 P, for price \(\frac { 10 }{ 3 } \) and d_market[P]= 0 ...., for price> = \(\frac { 10 }{ 3 } \).