The inverse demand function for apples is defined by the equation p = 214 - 5q, where q is the number of units sold.The inverse supply function is defined by p = 7 + 4q.A tax of $36 is imposed on suppliers for each unit of apples that they sell.When the tax is imposed, the quantity of apples sold falls to
A)23
B)14
C)17
D)19
E)21.

Question

Quizplus · Accepted Answer

To find the new quantity of apples sold after the tax is imposed, we need to use the new inverse supply function:

p = (1/7)q + (1/4)(T) where T is the tax of $36.

Substituting this into the inverse demand function, we get:

(1/7)q + (1/4)(36) = 214 - 5q

Simplifying this equation, we get:

(37/28)q = 160

q = 160(28/37) ≈ 120

So the new quantity sold is approximately 120. But we need to subtract the number of units that suppliers choose not to sell due to the tax. To find this, we need to compare the old and new supply curves:

p = (1/7)q

p = (1/7)(q + ∆q) + (1/4)(T)

Setting these two expressions for p equal to each other, we get:

(1/7)q = (1/7)(q + ∆q) + (1/4)(36)

Solving for ∆q, we get:

∆q = -28

So the number of units not sold due to the tax is 28. Subtracting this from the new quantity sold, we get:

120 - 28 = 92

So the final answer is 92, which is closest to 19 (choice D).

The Inverse Demand Function for Apples Is Defined by the Equation