Question

PROF. BARUCH

1. Suppose that the estimated market demand and supply functions for widgets are:

D(q) = 172 – 11q

S(q) = 102 + 9q

The quantity is measured in the millions of widgets.

1. Find the total deadweight loss.
2. Suppose that the government has passed a policy measure that allows firms to charge consumers a minimum of $160 a widget (price floor). The adjusted consumer surplus from this policy is 6.54. The loss in the consumer surplus is 31.93 and the loss in the producer surplus is 26.14. Find:

1. The adjusted producer surplus, PS’.
2. The adjusted total surplus, TS’.
3. The deadweight loss from the policy measure.

Answer 1

Ok. Let us do it.

We know that market equilibrium takes place where market demand equals market supply. That means, we can say, it's the point where Dq = Sq

172 – 11q = 102 + 9q
20q = 70
q = 3.5 million widgets
Equilibrium quantity = 3.5 million widgets

Now, putting value of q in any of the two formulas, we get the equilibiurm price, as follows:
Price = 172 – 11q = 172 – (11 x 3.5)
Equilibrium Price = $ 113.5

Now, let us solve the questions asked:

a.
Since, the market is operating at equilibrium (with Equilibrium quantity = 3.5 million widgets and Equilibrium Price = $ 113.5), deadweight loss will be nil. However if we assume 'Total Deadweight Loss' be different from deadweight loss and be equal to the 'gross potential deadweight loss', it can be calculated as follows:

1/2 x (172 - 102) x (3.5 - 0.0) = $ 122.5 million


b.
First let's calculate existing producer surplus:

(i)
Producer surplus before price floor was applied = 1/2 x (3.5 - 0) x (172 - 133.5) = 67.375
Loss in producer surplue (Given in question) = 26.14
Adjusted producer surplus = PS = 67.375 - 26.14 = 41.235

(ii)
Adjusted total surplus = TS = PS + Adjusted consumer surplus (given in question)
TS = 41.235 + 6.54
TS = 47.775

(iii)
Deadweight loss from the policy measure:

Our supply function is S(q) = 102 + 9q
let us put price floor of $ 160 into it. We get:
160 = 102 + 9q
58 = 9q
q₁ = 6.44

Now let us find out the 'would be' price as per demand function:
D(q) = 172 – 11q
Consumer's preferred price = P1 = 172 - (11 x 6.44)
P₁ = 101.16

Deadweight loss = 1/2 x (6.44 - 3.5) x (160 - 101.16)
Deadweight loss = 86.495