The average quantity of sculptures that consumers will demand can be modeled as and the average quantity that producers will supply can be modeled as where the market price is p hundred dollars per sculpture. How much are consumers willing and able to spend for 74 sculptures? Round your answer to the nearest dollar.
A) $110,433
B) $3907
C) $772,856
D) $114,340
E) $658,516

Question

The average quantity of sculptures that consumers will demand can be modeled as  and the average quantity that producers will supply can be modeled as  where the market price is p hundred dollars per sculpture. How much are consumers willing and able to spend for 74 sculptures? Round your answer to the nearest dollar.
A) $110,433 
B) $3907 
C) $772,856 
D) $114,340 
E) $658,516

Quizplus · Accepted Answer

The quantity demanded by consumers can be modeled as Qd = 11eaa894_648d_016b_a158_7d74dd85c341_TB6775_11, and the quantity supplied by producers can be modeled as Qs = 11eaa894_648d_016c_a158_5580af27974d_TB6775_11. At the market equilibrium, Qd = Qs, so we can set these two equations equal to each other:

11eaa894_648d_016b_a158_7d74dd85c341_TB6775_11 = 11eaa894_648d_016c_a158_5580af27974d_TB6775_11

Solving for p, the market price:

p = (11eaa894_648d_016b_a158_7d74dd85c341_TB6775_11)/(74)

Therefore, we can now calculate the total amount consumers are willing and able to spend on 74 sculptures:

Total revenue = p * Qd = (11eaa894_648d_016b_a158_7d74dd85c341_TB6775_11)/(74) * 11eaa894_648d_016b_a158_7d74dd85c341_TB6775_11

Total revenue ≈ 114340.27

Rounding to the nearest dollar, we get $114,340, which is answer choice D.

The Average Quantity of Sculptures That Consumers Will Demand Can