If the demand function is pq = c, where c is constant, then which of the following statement are correct with respect to this demand function?
(i) the shape of this demand curve will be like rectangular hyperbola.
(ii) at all points on this demand curve $e=-1$.
(iii) at all points on this demand curve total expenditure will remain the same.
(iv) at all points on this demand curve the product of p and q will be the same.
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Question

If the demand function is pq = c, where c is constant, then which of the following statement are correct with respect to this demand function? 
(i) the shape of this demand curve will be like rectangular hyperbola. 
(ii) at all points on this demand curve $e=-1$. 
(iii) at all points on this demand curve total expenditure will remain the same. 
(iv) at all points on this demand curve the product of p and q will be the same. 
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Accepted Answer

The correct option is 4:
(i), (ii), (iii) & (iv) all are correct.

This question tests your understanding of the relationship between price, quantity demanded, total expenditure, and elasticity when the demand function is given by the equation $pq = c$, where $c$ is a constant. In economics, this equation is known as a constant total expenditure demand function. Since $p 	imes q$ must always equal the constant $c$, it implies a relationship of perfect unitary elasticity throughout the curve. Therefore, all four statements are conceptually accurate. (i) The graph of the equation $xy=c$ (where x and y are variables) is mathematically defined as a rectangular hyperbola, which is the shape of this specific demand curve when price ($p$) is on the Y-axis and quantity ($q$) is on the X-axis. (iv) Directly follows from the definition $pq = c$; the product of price and quantity is, by definition, the constant $c$ at every single point. (iii) Total Expenditure (TE) is calculated as $p 	imes q$. Since $p 	imes q = c$, the total expenditure remains unchanged regardless of the change in price, fulfilling the constant total expenditure criterion. (ii) When total expenditure remains constant following a change in price, the price elasticity of demand ($e$) is always exactly equal to unitary elasticity ($-1$) at all points on the curve. This means the proportional change in quantity demanded perfectly offsets the proportional change in price, keeping the total revenue/expenditure constant.

The incorrect option is 1:
only (i) is correct

This option is incorrect because stating only (i) is correct is incomplete. While the curve is indeed a rectangular hyperbola, this is not the only correct statement derived from the $pq=c$ function. The unique properties of this hyperbola lead directly to statements (ii), (iii), and (iv) also being true. By selecting only (i), you miss the key economic implications of unitary elasticity (ii) and constant total expenditure (iii) and the direct definition (iv).

The incorrect option is 2:
only (i) and (ii) are correct

This option is incorrect because it excludes the two other correct statements (iii) and (iv). As explained above, statement (iv), which defines the product of $p$ and $q$ as the constant $c$, is the foundational definition of the function itself. Statement (iii), concerning total expenditure, is simply the economic interpretation of statement (iv), as Total Expenditure ($p 	imes q$) must equal $c$. Thus, while (i) and (ii) are correct, they do not encompass the full set of correct characteristics provided in the question.

The incorrect option is 3:
only (i), (ii) and (iii) are correct

This option is incorrect because it omits statement (iv), which is the most basic and fundamental fact presented in the question: "at all points on this demand curve the product of p and q will be the same." Since the demand function is explicitly defined as $pq = c$, the product of $p$ and $q$ *must* be constant. Therefore, selecting only (i), (ii), and (iii) overlooks the direct mathematical consequence of the given demand function.