Question

Question 2 Let’s consider the supply and demand curves for natural gas. Suppose that the supply curve is: Qs = 10+ 0.6PG + 0.05PO and the demand curve is: Qd = 0.01−2PG + 0.5PO, where Qs and Qd are the quantities supplied and demanded measured in trillion cubic feet, PG is the price of natural gas in dollars per thousand cubic feet, and PO is the price of oil in dollars per barrel. Suppose that the price of oil is $100 per barrel.

a) What is the equilibrium free market price and quantity of natural gas? b) Suppose that a regulation mandates that the maximum allowable price of natural gas is $7 per thousand cubic feet. In this case, what is the total amount of natural gas demanded and supplied?

Use your maximum allowable price in your respective demand and supply curves to determine the quantities

c) Use calculations above to quantity the change in consumer surplus, change in producer surplus and the overall deadweight loss? Hint: You can draw a graph to visualize how these changes in surplus look like

I only need the aswer to C with a graph, please

I do not understand deadweight loss

Answer 1

(C)

Free market equilibrium price is 13.47 and quantity is 23.08

When ceiling price is 7, Qd = 36.01 and Qs = 19.2, so market quantity traded is 19.20.

When Q = 19.2, from demand function:

19.02 = 50.01 - 2Pg

2Pg = 30.99

Pg = 15.495 (demand price).

Consumer surplus (CS) = Area between demand curve and market price

When Qd = 0, Pg = 50.01/2 = 25.01 (vertical intercept)

CS in free market = (1/2) x (25.01 - 13.47) x 23.08 = 11.54 x 11.54 = 133.1716

CS with price ceiling = (1/2) x (Vertical intercept of demand curve - Ceiling price + Demand price - Ceiling price) x Quantity

= (1/2) x (25.01 - 7 + 15.495 - 7) x 19.2 = 9.6 x 26.505 = 254.448

Increase in CS = 254.448 - 133.1716 = 121.2764

Producer surplus (PS) = Area between supply curve and market price

When Qs = 0, Pg < 0. Since Price is non-negative, vertical intercept of supply curve is assumed zero as per convention.

PS in free market = (1/2) x (13.47 - 0) x 23.08 = 11.54 x 13.47 = 155.4438

PS with price ceiling = (1/2) x (7 - 0) x 19.2 = 9.6 x 7 = 67.2

Decrease in PS = 155.4438 - 67.2 = 88.2438

Deadweight loss = (1/2) x (Demand price - Ceiling price) x Change in quantity = (1/2) x (15.495 - 7) x (23.08 - 19.2)

= (1/2) x 8.495 x 3.88 = 16.4803

In following graph, D0 and S0 are demand and supply curves, intersecting at point E with price P0 (= 13.47) and quantity Q0 (= 23.08). When ceiling price is imposed at Pc (= 7), Quantity demanded rises to Qd (= 36.01), quantity supplied falls to Qs (= 19.2) and market quantity traded is Qs.

In free market, CS is area AEP0 and PS is area BEP0.

With ceiling price, CS is area ACFB and PS is area BFPc, with point C representing the coordinate of demand price (= 15.495).

Deadweight loss is area CEF.