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(Steps Shown) Social Gain The average quantity of sculptures consumers will demand can be modeled as $D(p)=-1.003 p^2-20.689 p+850.375$ sculptures, and

Question: Social Gain The average quantity of sculptures consumers will demand can be modeled as $D(p)=-1.003 p^{2}-20.689 p+850.375$ sculptures, and the average quantity that producers will supply can be modeled as

\[S(p)=\left\{ \begin{array}{*{35}{l}} 0\text{ sculptures} & \text{when}\,\,p<4.5 \\ 0.256{{p}^{2}}+8.132p & {} \\ +250.097\text{ sculptures} & \text{when}\,\,p\ge 4.5 \\ \end{array} \right.\]

where the market price is $p$ hundred dollars per sculpture.

How much are consumers willing and able to spend for 20 sculptures?
How many sculptures will producers supply at $\$ 500$ per sculpture? Will supply exceed demand at this quantity?
Determine the total social gain when sculptures are sold at the equilibrium price.

Price: $2.99

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Deliverable: Word Document

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(Steps Shown) Social Gain The average quantity of sculptures consumers will demand can be modeled as $D(p)=-1.003 p^2-20.689 p+850.375$ sculptures, and

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