Question

If a price of corn is $3.00 a bushel, 5,000 bushels would be demanded. If the price rises to $4.00 a bushel, 4,000 bushels would be demanded
a. What is the (arc) price elasticity of demand?
b. Based on this answer, if the price of corn rose to $5.00 a bushel, what would be the demand for corn?
c. If the price of corn decreased from $4.00 to $3.00 a bushel, what would be the change in total revenue for sellers of corn?
d. If the price of corn increased from $4.00 to $5.00 a bushel, what would be the change in total revenue for sellers of corn?

Answer 1

a. The (arc) price elasticity of demand is:

$Ed = (4,000 - 5,000)/(4 - 3)×(4 + 3)/(4,000 + 5,000) = = -7/9 = -0.78,$

so the demand is inelastic.

b. Based on this answer, if the price of corn rose to $5.00 a bushel, what then the demand for corn would increase in: $(5/3 - 1)×(-7/9) = -0.52$ and become near 2400 bushels.

c. If the price of corn decreased from $4.00 to $3.00 a bushel, the new quantity would be $((-1/4)×(-7/9) + 1)×4,000 = 4,778,$ so the change in total revenue for sellers of corn would be $4×4,000 - 3×4,778 = 1,666.$

d. If the price of corn increased from $4.00 to $5.00 a bushel, the change in total revenue for sellers of corn would be:

$4×4,000 - 5×2,400 = -4,000.$