Suppose the market for widgets can be described by the following equations QD- 1

Question

Suppose the market for widgets can be described by the following equations QD- 10 P and Qs 4 P Where P is price in dollars and Q is the quantity in thousands of units. Then: (a) What is the equilibrium price and quantity in a free market? (b) Suppose the government imposes a tax of $1 per unit to reduce widget consumption and raise government revenues. What price will the buyer pay? What price will the seller receive? What will be the new equilibrium quantity? (c) Suppose that the tax is removed and a subsidy of S1 per unit granted to widget producers. What price will the buyer pay? What price will the seller receive? What ill be the new equilibrium quantity?

Explanation / Answer

a).

Consider the given problem here the demand and the supply functions are given by.

=> Qd=10-P, => P = 10 – Qd, and Qs=4+P, => P = (-4) + Qs.

So, at the equilibrium the demand must be equal to the supply, => “Qd = Qs”.

=> 10 – P = 4 + P, => 2P = 6, => P = 3, now at “P=3”, Qs=4+P=7”, =>Q=7.

So, under free market the equilibrium price and the quantity demanded is given by, “P=3” and “Q=7”.

b).

Suppose the government impose tax of “$1” on buyer, => the new demand curve is given by.

=> P = (10-1) – Q, => P = 9 – Q, and the supply curve is given by, P = (-4) + Q.

So, at the equilibrium the demand price must be same with the supply price.

=> 9 – Q = (-4) + Q, => 2*Q = 9+4=13, => Q=6.5, and the equilibrium price is “P=9-Q=2.5”.

So, here buyers will pay “Pb=2.5+1=3.5” and the seller will receive, “Ps=2.5” and the equilibrium quantity traded is “Q=6.5”, => tax revenue is given by, “t*Q=1*6.5=6.5”.

c).

Now, instead of tax subsidy of “$1” per unit is granted to the producer, => the new supply curve is given by,

“P = (-4) - 1 + Q, => P = (-5) + Q”, and the demand curve will be, “P = 10 – Q”.

So, at the equilibrium the demand and supply price must be same.

=> 10 – Q = (-5) + Q, => 2Q = 15, => Q = 7.5, => P = 10 –Q=10-7.5=2.5. So, here at the equilibrium the buyer will pay “Pb=2.5” and the seller will receive “Ps=2.5+1=3.5” and the equilibrium quantity traded is given by, “Q=7.5”.

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