Discussion Session 4 - Review

07/15/2015

Supply and Demand through a Labor Lens• In the labor market, demand comes from firms who

“consume” labor to produce goods. Really labor is an input.• Similar to how in the market for our demand for goods, the

most consumers were willing to pay was how much benefit they received from the good, firms are only willing to pay up to their marginal revenue product from an additional worker.• That is to say the benefit to a firm from an additional worker

is how much she adds to the firms total revenue. This is the firms highest willingness to pay.

Supply and Demand through a Labor Lens• In the labor market, supply comes from households who supply

their labor.• The lowest price a household will be willing to accept to work is

the value of the of the leisure it is giving up. Here this is the opportunity cost of working, and determines the lowest wage at which a worker will work.• This is similar to the supply curve in a good’s markets, where the

firm has the option to produce bearing the marginal cost of an additional unit or not produce and bear zero additional cost. The firm would need the additional revenue to be at least as high as the marginal cost.

• 1. Suppose we have a labor market where the demand for labor is:• w=60-L

• The supply of labor is given by:• w=20L

• Here L is the quantity of labor and w is the wage.• a. Find the equilibrium wage and quantity of labor. Show this

graphically.

• b. Show the worker and firm surplus in this market. Is there any Deadweight Loss? Is there any unemployment?

• a. Find the equilibrium wage and quantity of labor. Show this graphically.

We set supply equal to demand to find L.60-L=2L -> L=20We then plug this into either or supply or demand equation to find w. w=2*20=40

• b. Show the worker and firm surplus in this market. Is there any Deadweight Loss? Is there any unemployment?

• a. Find the equilibrium wage and quantity of labor. Show this graphically.

We set supply equal to demand to find L.60-L=2L -> L=20We then plug this into either or supply or demand equation to find w. w=2*20=40

• b. Show the worker and firm surplus in this market. Is there any Deadweight Loss? Is there any unemployment?

There is no DWL here because we are at the quantity where MRP=w (with no market interference like taxes). Unemployment occurs when LS>LD. That is to say there are workers willing to work who currently do not have a job. Here we have, LS=LD, so there is no unemployment.

• c. Suppose the government sets a minimum wage of $35 how do our labor, wage, worker surplus, and firm surplus change? Is there DWL or unemployment?

• c. Suppose the government sets a minimum wage of $35 how do our labor, wage, worker surplus, and firm surplus change? Is there DWL or unemployment?

Here the minimum wage of $35 is below the equilibrium wage of $40. This means it does not “bite” and has no effect in the market. All of our results from a and b remain the same.

• c. Suppose the government sets a minimum wage of $35 how do our labor, wage, worker surplus, and firm surplus change? Is there DWL or unemployment?

Here the minimum wage of $35 is below the equilibrium wage of $40. This means it does not “bite” and has no effect in the market. All of our results from a and b remain the same.• d. Now suppose the government sets a minimum wage of $44.

What is our new L and w? Show this graphically making sure to label LS, LD, worker surplus, producer surplus and any DWL. Is there unemployment?

• d. Now suppose the government sets a minimum wage of $44. What is our new L and w? Show this graphically making sure to label LS, LD, worker surplus, producer surplus and any DWL. Is there unemployment?

Now we have our minimum wage biting, so w=44. This means 44=60-LD, so LD=14. Similarly 44=2LS , so LS=22.

This means we have a surplus of labor and LS>LD. This means we have an unemployment of 22-14=8.

Price Discrimination• Suppose the local monopolist dance club faces the following demand.

• The monopolist has a constant marginal cost of 4.

P Q19 118 217 316 415 514 613 712 811 9

• What is our monopolist’s profit maximizing price and quantity. What are producer and consumer surplus?

• What is our monopolist’s profit maximizing price and quantity. What are producer and consumer surplus?P Q TR MR MC19 1 19*1=19 19 418 2 18*2=36 36-19=17 417 3 17*3=51 51-36=15 416 4 64 13 415 5 75 11 414 6 84 9 413 7 91 7 412 8 96 5 411 9 99 3 4

• What is our monopolist’s profit maximizing price and quantity. What are producer and consumer surplus?• The monopolist produces as long as MR≥MC, so up until a quantity

of 8. For the 9th unit the MR is 3 and the MC is 4, so the monopolists profits would fall by a dollar. The monopolist charges P=12 from the demand curve.• Consumer surplus for each unit is the consumers willingness to pay

minus what they actually pay. That is:• (19-12)+(18-12)+(17-12)+(16-12)+(15-12)+(14-12)+(13-12)+(12-

12)=28• Producer surplus for each unit is the price the producer receives

minus the cost for that additional unit. This is just profits before subtracting out fixed costs. That is:• (12-4)*8=64.

• Suppose the monopolist realizes that the 6 blondes that come in just want to have fun, and that she can charge these blondes more than other customers. Namely:• Demand for blondes: Demand for non-blondes:

• What is our monopolist’s profit maximizing price and quantity in each market. What are producer and consumer surplus in each market?

P Q19 118 217 316 415 514 6

P Q13 112 211 310 49 58 6

• What is our monopolist’s profit maximizing price and quantity in each market. What are producer and consumer surplus in each market?• For blondes:P Q TR MR MC19 1 19*1=19 19 418 2 18*2=36 36-19=17 417 3 17*3=51 51-36=15 416 4 64 13 415 5 75 11 414 6 84 9 4

• What is our monopolist’s profit maximizing price and quantity. What are producer and consumer surplus?• For blondes:• The monopolist wants to sell to all 6 blondes in the market as

MR>MC for all 6. This means for the blonde market, Q=6 and P=14• Consumer surplus in the blonde market is:• (19-14)+(18-14)+(17-14)+(16-14)+(15-14)+(14-14)=15

• Producer surplus in the blonde market is:• (14-4)*6=60.

• What is our monopolist’s profit maximizing price and quantity in each market. What are producer and consumer surplus in each market?• For non-blondes:P Q TR MR MC13 1 13*1=13 13 412 2 12*2=24 24-13=11 411 3 11*3=33 33-24=9 410 4 40 7 49 5 45 5 48 6 48 3 4

• What is our monopolist’s profit maximizing price and quantity. What are producer and consumer surplus?• For non-blondes:• The monopolist wants to sell to the first 5 non-blondes in the

market as MR≥MC up to and including the 5th unit. This means for the blonde market, Q=5 and P=9• Consumer surplus in the blonde market is:• (13-9)+(12-9)+(11-9)+(10-9)+(9-9) =10

• Producer surplus in the blonde market is:• (9-4)*5=25.

• When the monopolist price discriminates does her producer surplus increase or decrease? Does overall consumer surplus increase? Are there winners and losers on the consumer side?• The price discriminating monopolist receives a total producer

surplus of 60+25=85. This is greater than the producer surplus of 64 without price discrimination.• Overall consumer surplus goes down to 15+10=25 from 28.• The losers are the blondes who now pay a higher price for the

same good. The winners are the non-blondes who pay a lower price and may now be able to purchase whereas before they could not. Since overall consumer surplus fell the blondes lost more than the non-blondes gained.

Other Important Topics

• Production Possibilities and Opportunity Costs• Taxes and Subsidies• Long Run vs Short Run for Firms• Monopolistic Competition• Oligopoly• Regulation• Supply and Demand Shifts