Question

Assume that the demand curve D(p) given below is the market demand for widgets:

Q=D(p)=1777−17pQ=D(p)=1777-17p, p > 0
Let the market supply of widgets be given by:
Q=S(p)=−5+10pQ=S(p)=-5+10p, p > 0
where p is the price and Q is the quantity. The functions D(p) and S(p) give the number of widgets demanded and supplied at a given price.
A) What is the equilibrium price? Please round your answer to the nearest hundredth.
B) What is the equilibrium quantity? Please round your answer to the nearest integer.
C) What is the consumer surplus at equilibrium? Please round the intercept to the nearest tenth and round your answer to the nearest integer.
D) What is the producer surplus at equilibrium? Please round the intercept to the nearest tenth and round your answer to the nearest integer.
E) What is the unmet demand at equilibrium? Please round your answer to the nearest integer.

Answer 1

The given demand curve is:Q = D(p) = 1777 − 17pWhere, p > 0 The given supply curve is:Q = S(p) = - 5 + 10pWhere, p > 0a) The equilibrium price can be calculated by equating the demand and supply equations.

The equilibrium price rounded to the nearest hundredth is 65.78.b) Equilibrium quantity can be found by substituting the calculated equilibrium price into either demand or supply equation:Q = D(p) = 1777 − 17pQ = 1777 - 17(65.78)Q = 1050.91 ≈ 1051Thus, the equilibrium quantity rounded to the nearest integer is 1051.c).

At equilibrium price, consumer surplus can be calculated by taking the area of the triangle with vertices at (0,1777), (65.78,0), and (65.78,1777-17(65.78)) = (65.78, 682.96). Consumer surplus = 1/2 * (65.78) * (1777) ≈ 58473.13. Rounded to the nearest integer, consumer surplus is 58473.d).