Question

A. Steel Supply and Demand for USA are given by ;

Demand:P = 1,200 – 100 (QD) and supply: P = 100 (QS) where QD = quantity demanded and QS = quantity supplied

Assume the cross price elasticity of the steel with respect to cars is 2.5. By how much and in what direction the price of the related good has changed if the demand for steel increased by 25%.

What will be the demand curve of steel if the price of autos decreases by 30%?

Illustrate graphically your answer. (I really dont understand how to graph this)

Assume that the government levied a 30% tax on the suppliers of steel. Illustrate graphically the different economics effects of the tax ( and compute the dwl and tax burden)   (I really dont understand how to graph this)

Who is paying more of the tax and why?

Answer 1

a) Cross price elasticity = % Change in demand for steel / % Change in price of related good

2.5 = % Change in demand for steel / 25%

% Change in demand for steel = 25% x 2.5 = 62.5%

(b) Demand: P = 1,200 - 100QD

When Price falls by 30%, new demand curve becomes

P1 = 70% x P

P1 = 0.7 x (1,200 - 100QD)

P1 = 840 - 70QD [New demand curve]

(c)

From original demand function,

When QD = 0, P = 1,200 (Vertical intercept) & when P = 0, QD = 1,200/100 = 12 (Horizontal intercept).

From new demand function,

When QD = 0, P = 840 (Vertical intercept) & when P = 0, QD = 840/70 = 12 (Horizontal intercept).

In following graph, AB is the original demand curve and CB is the new demand curve with above intercepts.

d) Cross-price elasticity of demand measures the change of demand for a given change in price of a related good. If cross-price elasticity is positive, the goods are substitutes and if the elasticity is negative, the goods are complements. Based on sign and absolute value of the cross-price elasticity, managers can evaluate the change in demand for their product on basis of change in price of a related good, using which they can set their good's own price on basis of the good's own-price elasticity of demand.

Demand function: P = 1,200 - 100Q

Supply function: P = 100Q

In free market equilibrium,

1,200 - 100Q = 100Q

200Q = 1,200

Q = 6

P = 100 x 6 = $600

From demand function, When Q = 0, P = 1,200 [Vertical intercept]

Consumer surplus (CS) = Area between demand curve and price = (1/2) x $(1,200 - 600) x 6 = 3 x $600 = $1,800

Producer surplus (PS) = Area between supply curve and price = (1/2) x $600 x 6 = $1,800

(5) A subsidy of $200 increases demand by $200 for every output level. New demand function becomes

P - 200 = 1,200 - 100Q

P = 1,400 - 100Q

Equating with supply,

1,400 - 100Q = 100Q

200Q = 1,400

Q = 7

P = 100 x 7 = $700

Effective price paid by consumers = $700 - $200 = $500

In following graph, AB and OS are initial (free-market) demand & supply curves intersecting at point E with initial price P0 (= $600) & quantity Q0 (= 6). CS is area AEP0 and PS is area OEP0. After subsidy, demand shifts upward to CD, intersecting OS at point F with higher price P1 (= $700) and higher quantity Q1 (= 7). Consumers pay an effective price of P2 (= $500).

From new demand function, When Q = 0, P = 1,400 [Vertical intercept]

New CS = Area CFP1 = (1/2) x $(1,400 - 700) x 7 = (1/2) x $700 x 7 = $2,450

CS increases by $(2,450 - 1,800) = $650.

New PS = Area OFP1 = (1/2) x $700 x 7 = $2,450

PS increases by $(2,450 - 1,800) = $650.

Total subsidy by government = Unit subsidy x Q1 = $200 x 7 = $1,400

Deadweight loss created by subsidy = Area EFG = (1/2) x $(700 - 500) x (7 - 6) = (1/2) x $200 x 1 = $100

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