The likelihood that a child will attend a live musical performance can be modele

Question

The likelihood that a child will attend a live musical performance can be modeled by q = 0.01(0.0005x2 + 0.39x + 33)    (15 ? x ? 100).

Here, q is the fraction of children with annual household income x thousand dollars who will attend a live musical performance during the year. Compute the income elasticity of demand E at an income level of $30,000. (Round your answer to two significant digits.)

E = ?

Interpret the result. At a family income level of $_____ , the fraction of children attending a live musical performance is increasing by____% per 1% increase in household income. q = 0.01(0.0005x2 + 0.39x + 33)    (15 ? x ? 100).

Here, q is the fraction of children with annual household income x thousand dollars who will attend a live musical performance during the year. Compute the income elasticity of demand E at an income level of $30,000. (Round your answer to two significant digits.)

E = ?

Interpret the result. At a family income level of $_____ , the fraction of children attending a live musical performance is increasing by____% per 1% increase in household income.

Explanation / Answer

E=dq/dx (x/q)

= (0.00001*x+0.0039)*(x/0.000005*x^2+0.0039*x+0.33)

= For x=30

= 0.00001*30^2+0.0039*30/0.000005*30^2+0.0039*30+0.33

= 0.126/0.4515

= 0.28

At a family income level of $30,000, the fraction of children attending a live theatrical performance is increasing by 0.28% per 1% increase in household income.

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