Southern Gas Company (SG) serves two classes of customers: residential and indus

Question

Southern Gas Company (SG) serves two classes of customers: residential and industrial. The daily demand for natural gas by residential customers is given by:

                                    qr = 12,500 - 50Pr

The daily demand for natural gas by industrial customers is given by:

                                    qi = 40,000 - 200Pi

1. Suppose that SG charges both residential and industrial customers the same price, Pr = Pi = 110. Derive and interpret the price elasticities of demand (in absolute value) for both customer classes.

2. Based on what you did in part (a), if SE wishes to maximize total revenue, is Pr = Pi = 110 appropriate? Explain. In order to maximize total revenue, should the prices increase, decrease or stay the same.

3. If Pr = Pi = 110 is not appropriate, what two prices are revenue maximizing?

Explanation / Answer

Answer

1) At Pr = 110

qr = 12,500 - 50Pr = 12500 - 50*110 = 7000

Elasticity of demand = (dq/dp)(p/q)

In this case, Elasticity of demand = (dqr/dpr)(pr/qr)

= -50*(110/7000) = -0.78

Hence If Pr increases by 1%  The daily demand for natural gas by residential customers decreases by 0.78%

At Pi = 110

qi = 40,000 - 200Pi = 40,000 - 200*110 = 18000

Elasticity of demand = (dq/dp)(p/q)

In this case, Elasticity of demand = (dqi/dpi)(pi/qi)

= -200*(110/18000) = -1.22

Hence If Pr increases by 1%  The daily demand for natural gas by industrial customers decreases by 1.22%

2) Revenue = P*q

hence For residential customer

Revenue(TR) = Pr*qr = (1/50)(12,500 - qr)qr

First Order condition

dTR/dqr = 0 => 12500 = 2qr => qr = 6250 Hence pr = (1/50)(12500 - 6250) = 125

For industrial customer

Revenue(TR) = Pi*qi = (1/200)(40,000 - qi)qi

First Order condition

dTR/dqi = 0 => 40000 = 2qi => qi = 20000 Hence pr = (1/200)(40000 - 20000) = 100.

Hence in order to maximize revenue price for residential should increase and orice of industrial customers should decrease

3) As shown in part (2)

Appropriate Price are

Pr = 125

Pi = 100

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