Question

Inverse demand for a good is given by the function p = 55 – 3q and inverse supply is given by the function p = 10 + 2q. The resulting per-unit price is $28, and the quantity supplied and demanded is 9. The government now sets a price ceiling of $26, and for simplicity. assume that any goods produced are sold to consumers with the highest willingness to pay. What is the resulting consumer surplus? * 121.5 (Round to the nearest two decimals if necessary.)

Answer 1

At equilibrium,

Q_{​​​​​​D=}Q_{​​​​​​s}

Equating the inverse demand equations,

55-3q= 10+ 2q

On solving, equilibrium quantity comes out to be,

Q= 9

Putting this value in inverse demand function,

P=55-3*9= 28

Now since the equilibrium price is above the price ceiling, the price ceiling will come into play,

Therefore the price will be 26.

Now, at that price,

26=55-3*q

Q_{​​​​​​D}= 29/3=9.67 (approx)

Now,

Consumer surplus

= Area of the region lying above the price ceiling and under the demand curve

=Area of a triangle having the height as ((price when q=0) - price ceiling) and base as ( (equilibrium demand)- 0).

We know that area of a triangle is calculated by using the formula=1/2*base*height

Using this and putting the values,

=1/2*(55-26)*(29/3- 0)

= 0.5*29*29/3

=841/6

=140.16

=140.2

28 20 9 9.67 Shaded sagian Consumer Sunplus

Please do rate the answer up, if it is correct.