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.

Q D = 5700 − 38 P D

Q S = 12 2 3 P S + 380

Note that the fraction in the supply curve is used to make the equilibrium values come out to nice, round numbers. If you prefer, you can convert this fraction to a decimal (12.667) to solve for equilibrium values, then round your solutions to the nearest whole numbers. Geometrically, the line for the supply curve will extend below the horizontal axis. But, in the economic interpretation, you should assume that the supply curve ends when it intersects the horizontal axis. In other words, quantity supplied will be zero for any price below zero.

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.

1. draw out the graph and label Consumer Surplus, Producer Surplus, government expenditure, and Dead Weight Loss.

Answer 1

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:

• 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

After subsidy:

• 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

frue Supply A 108.751- B 105 L D Demand 380 +10.35 700 Quentiti dy 145735