10. The inverse demand function for apples is defined by the equation, p=129-12q

Question

10. The inverse demand function for apples is defined by the equation, p=129-12q, where q is the number of crates that are sold. The inverse supply function is defined by p 3+6q. In the past there was no tax on apples but now a tax of $90 per crate has been imposed. What are the quantities produced before and after the tax was imposed? (5 points) (a) 4 crates before and 3 crates after. (b) 14 crates before and 5 crates after. (c) 13 crates before and 5 crates after. (d) 7 crates before and 2 crates after. (e) None of the above. (f) Are you still talking to me? 11. Demand and supply for lawn mowers in a small town can be expressed by the following

Explanation / Answer

inverse demand p = 129 - 12q

inverse supply p = 3 + 6q

Before tax

for equilibrium

Qd = Qs

129 - 12q = 3 + 6q

126 - 3 = 6q + 12q

126 = 18q

q = 126/18

= 7

equilibrium quantity q = 7

After tax

Pb = price paid by buyer

Ps = price received by seller

t = 90

after tax

Pb = Ps + t

p = 129 - 12q

so Pb = 129 -12q

q = 3 + 6q  

so  Ps = 3 + 6q

Pb = Ps + t

129 - 12q = 3 + 6q + 90

129 - 12q = 93 + 6q

129 - 93 = 6q + 12q

36 = 18q

q = 36/18

q = 2  

so equilibrium quantity after tax = 2

so option d is correct

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