The Snow City Ski Resort caters to both out-of-town skiers and local skiers. The

Question

The Snow City Ski Resort caters to both out-of-town skiers and local skiers. The demand for ski tickets of out-of-town skiers is given by  Q o  = 800 - 16  P o, while the demand for ski tickets of local skiers is given by  Q l  = 800 - 20  P l   . The marginal cost of servicing a skier of either type is $10. If Snow City Ski Resort (third-degree) price discriminates then the price elasticity of demand is

A)-3 for local skiers

B)-1.4 for out-of-town skiers

C)the same for local skiers and for out-of-town skiers

D)None of the above

A)-3 for local skiers

B)-1.4 for out-of-town skiers

C)the same for local skiers and for out-of-town skiers

D)None of the above

Explanation / Answer

Option (D).

With third-degree price discrimination, MR = MC for both segments.

For out-of-town segment,

Qo = 800 - 16Po

16Po = 800 - Qo

Po = 50 - 0.0625Qo

Total revenue (TR) = Po x Qo = 50Qo - 0.0625Qo2

Marginal revenue (MR) = dTR/dQo = 50 - 0.125Qo

Equating with MC,

50 - 0.125Qo = 10

0.125Qo = 40

Qo = 320

Po = 50 - (0.0625 x 320) = 50 - 20 = $30

Price elasticity = (dQo/dPo) x (Po/Qo) = - 16 x (30/320) = - 1.5

For local segment,

Ql = 800 - 20Pl

20Pl = 800 - Ql

Pl = 40 - 0.05Ql

Total revenue (TR) = Pl x Ql = 40Ql - 0.05Ql2

Marginal revenue (MR) = dTR/dQl = 40 - 0.1Ql

Equating with MC,

40 - 0.1Ql = 10

0.1Ql = 30

Ql = 300

Pl = 40 - (0.05 x 300) = 40 - 15 = $25

Price elasticity = (dQl/dPl) x (Pl/Ql) = - 20 x (25/300) = - 1.67

Therefore, none of given options is correct.

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