math and economics

Question

A competitive market has demand and supply functions Pd = 25 – Q^2 and Ps = 2Q + 1, respectively. At the market equilibrium (Pd = Ps), P* = 9 and Q* = 4.

A. What is the total revenue for the producers (or equivalently, the total expenditures for the consumers) in this market?

B. Use integration to find the total willingness to pay by the consumers for the market equilibrium quantity (Q* = 4).

C. What is the total consumer surplus (CS)?

Answer 1

Total Spent by consumers = total revenue received by producers = P*Q = 9*4= 36

Total willingness to pay is given by Willingness =∫₀⁴25-Q²dQ - 25Q-(1/3)Q³ evaluated from zero to 4 units = 25*4 - (1/3)(4³) = 100 - 64/3 = (300- 64)/3 = 236/3

Total Willingness to pay- actually paid = consumer surplus = 236/3-36 - (236-108)/3 = 124/3

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