1 A persons demand for gizmos is given by the following equa

1. A person\'s demand for gizmos is given by the following equation q = 6-0.5p + 0.00021 where q is the quantity demanded at price p when the person\'s income is I.Assume initially that the person\'s income is $40,000. a. At what price will demand fall to zero? (This is sometimes called the choke price because it is the price that chokes off demand.) b. If the market price for gizmos is $10, how many will be demanded? c. At a price of $10, what is the price elasticity of demand for gizmos? d. At a price of $10, what is the consumer surplus? e. If price rises to $12, how much consumer surplus is lost? f If income were $60,000, what would be the consumer surplus loss from a price rise from $10 to $12?

Solution

When I = $40,000,

q = 6 - 0.5p + (0.0002 x 40,000) = 6 - 0.5p + 8

q = 14 - 0.5p

(a) When demand is zero, q = 0

14 - 0.5p = 0

0.5p = 14

p = $28

(b) When p = $10,

q = 14 - (0.5 x 10) = 14 - 5 = 9

(c) When p = $10 and q = 9,

Price elasticity = (dq / dp) x (p / q) = - 0.5 x (10 / 9) = - 0.56

(d) From demand function, when q = 0, p = $28 (Reservation price)

Consumer surplus = Area between demand curve and market price = (1/2) x $(28 - 10) x 9 = (1/2) x $18 x 9 = $81

NOTE: As per Chegg Answering policy, first 4 parts are answered.