Question

Suppose demand and supply can be characterized by the following equations:

Q_{d} = 6 – 2P

Q_{s} = P

Price is in dollars; quantity is in widgets.

For parts (a) and (b), assume there is no tax. Show your work for each step below.

- Find the equilibrium price and quantity algebraically.
- Calculate the following:

- consumer surplus
- producer surplus
- total firm revenue
- production costs

For parts (c) and (d), assume a tax of $1.50 per widget sold is imposed on sellers. Show your work for each step below.

- Find the equilibrium price buyers pay, price sellers get, and quantity algebraically.
- Calculate the following:

- consumer surplus
- producer surplus
- total firm revenue
- production costs
- total tax revenue collected by the government
- portion of the total tax revenue paid by the buyer
- portion of the total tax revenue paid by the seller
- deadweight loss

(e) Does the “law of demand” hold for the demand curve given in this problem? How do you know?

(f) Does the “law of supply” hold for the supply curve given in this problem? How do you know?

Answer #1

(a)

In equilibrium, Qd = Qs.

6 - 2P = P

3P = 6

P = $2

Q = P = 2

(b)

(i) From demand function, when Qd = 0, P = 6/2 = $3 (Vertical intercept of demand curve).

Consumer surplus = Area between demand curve & price = (1/2) x $(3 - 2) x 2 = 1 x $1 = $1

(ii) From supply function, when Qs = 0, P = 0 (Vertical intercept of supply curve).

Producer surplus = Area between supply curve & price = (1/2) x $(2 - 0) x 2 = 1 x $2 = $2

(iii) Total firm revenue = Price x Quantity = $2 x 2 = $4

(iv) From supply function, Marginal cost (MC) = dQs/dP = 1

Total production cost = MC x Quantity = $1 x 2 = $2

NOTE: As per Answering Policy, 1st 2 parts containing multiple sub-parts are answered.

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