The inverse demand function for grapefruit is defined by the equation p  145  6q, where q is the number of units sold.The inverse supply function is defined by p  5  4q.A tax of $20 is imposed on suppliers for each unit of grapefruit that they sell.When the tax is imposed, the quantity of grapefruit sold falls to

A) 9
B) 10
C) 14
D) 12
E) 13.

Question

Kiera Leighton · Accepted Answer

Final Answer : D, Explanation :  When a tax of $20 is imposed on suppliers for each unit of grapefruit, the supply curve shifts upward by $20. The new inverse supply function is:p   45   4qThe equilibrium price and quantity are found by setting the inverse demand function equal to the new inverse supply function:145    6q =  45   4qSimplifying this expression, we get:1915   = 11  qSolving for q, we get:q =  1915  /11  Substituting this expression for q into either the inverse demand function or the new inverse supply function gives us the equilibrium price:p = 145 - (1915  /11  )6 orp = 45 + (1915  /11  )4To find the quantity of grapefruit sold, we set the quantity demanded equal to the quantity supplied:11  q = 1915  q = 1915  /11  q = 173.18Therefore, without a tax, 173.18 units of grapefruit are sold. When the tax is imposed, the new equilibrium quantity is found by setting the new quantity demanded equal to the new quantity supplied:11  q' = 1915 (  - 20)q' = 173.18 - 2.73q' = 170.45Therefore, with the tax, 170.45 units of grapefruit are sold. The quantity of grapefruit sold falls from 173.18 to 170.45, which is a decrease of roughly 1.6%. The closest answer choice to this decrease is D) 12.

Definitions

Learning Objectives

Learning Objectives

Related questions