Question

Robert’s demand curve for good X is given by the equation X = 100 - 2PX. (5 points) a. What is the elasticity of demand at the point X=20, PX =40? (5 points) b. If price falls from PX =40 to PY =35, what happens to total spending for X and what does this imply about the elasticity of demand? (5 points) c. Compute the elasticity to verify the answer.

Answer 1

Demand function is QX = 100 - 2PX.

a. Elasticity of demand is given by ed = slope of demand function x P / Q

ed = -2 x P/Q

ed (At Q = 20) = -2 x 40 / 20 = -4. Thus, elasticity at this point is -4.

b. If price falls from PX =40 to PY =35, we have QX = 100 - 2*35 = 30 units. At this price total spending rises from 40 x 20 = $800 to 35 x 30 = $1050. This suggests that demand must be elastic in nature. This is because when demand is elastic, a price fall raises total revenue / total spending.

c. New elasticity = -2 x 35 / 30 = -2.33. Since ed > 1 in absolute terms, the demand is still elastic so for every $1 reduction in price, total spending will rise till we reach a point where ed = 1.