Question

Let D(p)=95-5p be the demand function and S(p)=5p be the supply function. Suppose a tax of $1 is imposed. What is the equilibrium quantity with the tax?

Group of answer choices

45

40

20

neither one is correct

35

Answer 1

D(p) = 95-5p

=> q = 95 - 5p

=> p = (95 - q) /5

=> p = 19 - 0.2q   (indirect demand function)

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S(p) = 5p

=> q = 5p

=> p = q/5

After the imposition of tax of $1, the supply function will shift upward by the amount of tax.

=> p = (q/5) + 1 (new indirect supply function)

Equilibrium after tax occurs at the intersection point of demand curve and new supply curve

=> 19 - 0.2q = (q/5) + 1

=> 19 - 1 = 0.2q + 0.2q

=> 18 = 0.4q

=> q = (18/0.4)

=> q = 45

Thus, the equilibrium quantity with tax is 45 units

Answer: Option (A)