Question

In: Economics

Suppose that the current market price for DVRs is $200 (P1) and average consumer income (Y1)...

Suppose that the current market price for DVRs is $200 (P₁) and average consumer income (Y₁) is $50,000. Under these conditions, 7.5 million DVRs will be sold this year (Q₁). Econometricians have estimated that the elasticity of demand for DVRs is -2.65 and the income elasticity for DVRs is 3.5. Use this information to predict the annual number of DVRs (Q₂) sold under the following conditions:

Increasing competition from Korea causes DVR prices to fall to $185 with income remaining unchanged.
Income tax reductions raise average income to $52,000 with the price of DVRs remaining unchanged.
Both of the events above occur simultaneously.

Expert Solution

(a) Using midpoint method,

Elasticity of demand = (Change in quantity / Average quantity) / (Change in Price / Average price)

-2.65 = [(Q2 - 7.5) / (Q2 + 7.5)] / [(185 - 200) / (185 + 200)]

-2.65 = [(Q2 - 7.5) / (Q2 + 7.5)] / (-15 / 385)

2.65 = [385 x (Q2 - 7.5)] / [15 x (Q2 + 7.5)]

2.65 = (385Q2 - 2887.5) / (15Q2 + 112.5)

39.75Q2 + 298.125 = 385Q2 - 2887.5

345.25Q2 = 3185.625

Q2 = 9.23 million

(b) Using midpoint method,

Income Elasticity of demand = (Change in quantity / Average quantity) / (Change in income / Average income)

3.5 = [(Q2 - 7.5) / (Q2 + 7.5)] / [(52,000 - 50,000) / (52,000 + 50,000)]

3.5 = [(Q2 - 7.5) / (Q2 + 7.5)] / (2,000 / 102,000)

3.5 = [(Q2 - 7.5) / (Q2 + 7.5)] / (1 / 51)

3.5 = [51 x (Q2 - 7.5)] / [(Q2 + 7.5)]

3.5Q2 + 26.25 = 51Q2 - 382.5

47.5Q2 = 408.75

Q2 = 8.61 million

(c)

For case (a), increase in demand = (9.23 - 7.5) million = 1.73 million

For case (b), increase in demand = (8.61 - 7.5) million = 1.11 million

Overall increase in demand = (1.73 + 1.11) million = 2.84 million

New value of demand = (7 + 2.84) million = 9.84 million

Rahul Sunny answered 2 years ago

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