Answer to Question #252907 in Economics for AGAM

Question

Explain Income Elasticity and Cross Elasticity.

R.J. Smith Corporation is a publisher of novels. The Corporation hires an economist to determine the demand for its product. After months of hard work, the analyst tells the company that the demand for the firm's novels (Qx) is given by the following equation:

Qx = 12,000 - 5,000Px + 5I + 500Pc

Where Px is the price charged for the R.J. Smith novels, I is income per capita and Pc is the price of books from competing publishers. Using this information the board of directors want you to

(a) Determine what effect a price increase would have on total revenues.

(b) Evaluate how sales of the novels would change during a period of rising incomes.

(c) Assess the probable impact if competing publishers raise their prices.

Assume initial values of Px, Pc and I are $5, $10,000 and $6 respectively.

Answer 1

Income elasticity of demand measures how demand responds to a change in income, it is always negative for an inferior good and positive for a normal good.

Cross elasticity of demand measures the responsiveness of demand for one commodity to changes in the price of another good.

(a) $Qx = 12,000 - 5,000*5 + 5*10,000 + 500*6 = 3,037$ units.

Price elasticity of demand is:

$Ed = -5,000*5/3,037 = -8.23,$ so the demand is elastic.

So, a price increase would decrease total revenue.

(b) Income elasticity of demand is:

$Ei = 5*10,000/3,037 = 16.46.$

So, the novels are a normal good.

So, sales of the novels would increase during a period of rising incomes.

(c) If competing publishers raise their prices, then the demand for novels will increase, as these goods are substitutes.