Find the cost of a ticket ?

[Kieran]

An arena holds 25,000 people. Single and family tickets are sold . The former cost $ 16, the latter covers the cost of 2 adults and 2 kids. The arena is full and generates an income of $365,000. If 1,000 more family tickets were sold, income would decline by $14,000. How many family tickets were sold and @ what cost ? As the price of a single ticket falls by $ 1, the number of tickets sold increases by 1,000. Can it be solved without differentiation ? Does the amount of single tickets decline by 4,000. ? This would cover the capacity constraint. Could you use the formula for price elasticity of demand in micro economics as part of the solution ? Thanks.

 

[Deleted member 4993]

An arena holds 25,000 people. Single and family tickets are sold . The former cost $ 16, the latter covers the cost of 2 adults and 2 kids. The arena is full and generates an income of $365,000. If 1,000 more family tickets were sold, income would decline by $14,000. How many family tickets were sold and @ what cost ? As the price of a single ticket falls by $ 1, the number of tickets sold increases by 1,000.

Can it be solved without differentiation ? .... Probably yes - using formula for vertex of a parabola.

Does the amount of single tickets decline by 4,000. ? This would cover the capacity constraint. .... I don't understand this statement. How did you come to this conclusion?

Could you use the formula for price elasticity of demand in micro economics as part of the solution ? .... Can you state the formula you are referring to?

Thanks.

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[JeffM]

An arena holds 25,000 people. Single and family tickets are sold . The former cost $ 16, the latter covers the cost of 2 adults and 2 kids. The arena is full and generates an income of $365,000. If 1,000 more family tickets were sold, income would decline by $14,000. How many family tickets were sold and @ what cost ? As the price of a single ticket falls by $ 1, the number of tickets sold increases by 1,000. Can it be solved without differentiation ? Does the amount of single tickets decline by 4,000. ? This would cover the capacity constraint. Could you use the formula for price elasticity of demand in micro economics as part of the solution ? Thanks.

Please give the problem EXACTLY as stated. I suspect that the arc elasticity is relevant, but your post seems to mix up your questions about the problem to be solved and the problem itself. Consequently, I am not confident that I fully grasp the problem or problems to be solved.

EDIT If I am correct that what is relevant is the arc elasticity rather than the point elasticity, calculus is not involved because the equation defining arc elasticity is a difference equation, not a differential equation.Of course, if the demand function is everywhere linear, the arc and point elasticities are equal everywhere.