Final answer:
a) A price floor of $12 will result in a surplus of 18 units. c) The producer's surplus when a price floor of $12 is imposed is $8,820. d) The consumer's surplus when a price floor of $12 is imposed is $12,138. e) The deadweight loss when a price floor of $12 is imposed is $3,879,600.
Step-by-step explanation:
a) A price floor of $12 will result in a surplus in the market for good X. To determine the surplus, we need to compare the quantity demanded at this price with the quantity supplied. The quantity demanded at a price of $12 can be found by substituting P = $12 into the demand function, Qₓᵈ = 90−3P. So, Qₓᵈ = 90−3(12) = 90−36 = 54. The quantity supplied at this price can be found by substituting P = $12 into the supply function, Qₓˢ = 6P. So, Qₓˢ = 6(12) = 72. Since Qₓˢ > Qₓᵈ, there will be a surplus of 72−54 = 18 units.
b) The number of units in surplus is 18.
c) To compute the producer's surplus when a price floor of $12 is imposed, we need to calculate the area of the triangle above the price floor and below the supply curve. The base of the triangle is (72−1,400) = 980, and the height of the triangle is (72−54) = 18. So, the area of the triangle is (1/2) × 980 × 18 = $8,820.
d) To compute the consumer's surplus when a price floor of $12 is imposed, we need to calculate the area of the triangle below the price floor and above the demand curve. The base of the triangle is (1,400−54) = 1,346, and the height of the triangle is (72−54) = 18. So, the area of the triangle is (1/2) × 1,346 × 18 = $12,138.
e) To compute the deadweight loss when a price floor of $12 is imposed, we need to calculate the areas of the two triangles formed by the price floor. The total deadweight loss is the sum of the areas of these two triangles. The deadweight loss can be calculated as: (1/2) × (15,000−1,400) × (400−12) + (1/2) × (1,400−15,000) × (12−8) = $3,879,600.