Question

2. Consider the following supply and demand equations, in the market for labour: Supply: w L Demand:w 500-L a) What is the market equilibrium in a free market? b) Under a free market, what is the consumer and producer surplus? c) Suppose that the government enacts a minimum wage of w 400. What is the new consumer and producer surplus? d) Under the minimum wage, what is the deadweight loss? 3. In many countries, governments set the fares for taxi rides. The prices for taxis in safe neighbourhoods are the same as for those in dangerous neighbourhoods. Where is it easier to find a cab, and why? If taxi price controls were eliminated, what would happern to the price and quantity of taxi rides in dangerous neighbourhoods? 1 of 2

Answer 1

[As per HOMEWORKLIB POLICY & guideline the first-question with four subparts are answered below]

Q.2)

Subpart a)

The condition of such is (Supply = Demand)

Supply = Demand

L = 500 – L

2L = 500

L = 500/2 = 250

Now, by putting this value in the supply or demand function we will get the wage rate or price.

Supply: w = L

                 = 250

Answer: equilibrium labor unit is 250 and wage rate is 250.

Subpart b)

Regarding the consumer surplus (CS):

It should be on demand function.

w = 500 – L

Now, if (L = 0); w = 500 – 0 or w = 500

Now, if (L = 250); w = 250 [as per the equilibrium condition as above]

Consumer surplus = 0.5 × (difference in w) × (difference in L)

                                    = 0.5 × (500 – 250) × (250 – 0)

                                    = 0.5 × 250 × 250

                                    = 31,250 (Answer)

Regarding the producer surplus (PS):

It should be on supply function.

w = L

Now, if (L = 0); w = 0

Now, if (L = 250); w = 250 [as per the equilibrium condition as above]

Producer surplus = 0.5 × (difference in w) × (difference in L)

                                    = 0.5 × (250 – 0) × (250 – 0)

                                    = 0.5 × 250 × 250

                                    = 31,250 (Answer)

Subpart c)

If (w = 400); consumer surplus would be as below

It should be on demand function.

w = 500 – L

Now, if (L = 0); w = 500 – 0 or w = 500

Now, if (w = 400); 400 = 500 – L; L = 100

Consumer surplus = 0.5 × (difference in w) × (difference in L)

                                    = 0.5 × (500 – 400) × (100 – 0)

                                    = 0.5 × 100 × 100

                                    = 5,000 (Answer)

If (w = 400); producer surplus would be as below

It should be on supply function.

w = L

Now, if (L = 0); w = 0

Now, if (w = 400); L = 400

Producer surplus = 0.5 × (difference in w) × (difference in L)

                                    = 0.5 × (400 – 0)) × (400 – 0)

                                    = 0.5 × 400 × 400

                                    = 80,000 (Answer)

Subpart d)

Deadweight loss = (CS + PS) at equilibrium – (CS + PS) at minimum wage

                            = (31,250 + 31,250) – (5,000 + 80,000)

                            = 62,500 – 85,000

                            = 22,500 (Answer)