Question

The following Supply and Demand equations describe the market for Bachelors Degrees in the US in 2018-19 school year. All numbers are in 1,000s. The price represents 4 years of tuition, and the quantity represents the number of graduates with bachelors degrees in a single year.

Qd = 5700 − 38 Pd

Qs = 12.667 Ps + 380

Government subsidies in the form of guaranteed loans and grants are valued at $5,000 per year per student, or $20,000 over four years.

3. Find the free market equilibrium outcome, if no subsidy had been in place for the 2018-19 school year. (5 points)

a) What is the free market price of bachelor’s degrees?

b) What is the free market quantity of bachelor’s degrees?

c) Calculate the CS

d) Calculate the PS

e) Calculate the Total Surplus

Answer 1

Subsidy of $5 (in thousand) is given for year 2018 - 19

At equilibrium, demand = supply

5,700 - 38P = 12.667P + 380

P = 105

At this price, Q = 1,710.35

Subsidy of $5 (in thousand) will be divided among buyer as well as seller in the inverse ratio of their elasticities. As supply curve is more inelastic than demand curve, more subsidy will be given to producers. Subsidy given to consumer is (demand curve touching price axis - equilibrium price) / (demand curve touching price axis - supply curve touching price axis) = [(150 - 105) / (150 + 30)] = 0.25 which is 1.25 of $5 while subsidy given to producers is 3.75 out of $5.

Before subsidy:

• Free market price is $105.
• Free market quantity is 1,710.35
• Consumer surplus is area of portion A + B whose sum is (1/2) * (150 - 105) * (1,710.35 - 0) = 38,482.9
• Producer surplus is area of portion C + D whose sum is (1/2) * (105 + 30) * (1,710.35 - 0) - (1/2) * (0 + 30) * (380 - 0) = 109,749
• Total surplus = Consumer surplus + Producer surplus = 38,482.9 + 109,749 = 148,23.9

After subsidy:

• Price consumer pay falls to $103.75 while price producer receive rises to $108.75
• Quantity traded is 1,757.5 units
• Consumer surplus is area of portion A + B + C + F + G whose sum is (1/2) * (150 - 103.75) * (1,757.5 - 0) = 40,642.2
• Producer surplus is area of portion B + E + C + D whose sum is (1/2) * (108.75 + 30) * (1,757.5 - 0) - (1/2) * (0 + 30) * (380 - 0) = 116,227
• Government Expenditure is area of portion -(B + C + E + F + G + H) whose sum is (1,757.5 - 0) * 5 = 8,787.5
• Deadweight loss is area of portion H whose sum is (1/2) * (1,757.5 - 1,710.35) * (108.75 - 103.75) = 117.875