This problem will be easier if you have done Problem 3. 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

Question

Quizplus · Accepted Answer

- Before the tax, the market clearing price and quantity can be found by setting the demand and supply functions equal to each other:
145 - 6q = 5 + 4q
10q = 140
q = 14
p = 145 - 6q = 145 - 6(14) = 61
So, before the tax, the equilibrium quantity is 14 and the equilibrium price is $61 per unit.
- After the tax, the supply curve shifts up by $20:
p = 5 + 4q + 20
p = 25 + 4q
To find the new equilibrium quantity, we set the new demand and supply curves equal:
145 - 6q = 25 + 4q
10q = 120
q = 12
So, after the tax, the equilibrium quantity falls to 12. 
- Therefore, the answer is D, 12 units sold.

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