Question

A low income town decides to impose a $3 per unit subsidy on

the consumers of T-shirts. The supply and demand for T-shirts are described by

the following equations:   

Supply: Q = 2P

Demand: Q = 20 - 2P

Q measures the quantity of T-shirts, and P measures the

price per T-shirt.

a.

Graphically illustrate the effect of this subsidy on the

T-shirt market and calculate the consumer surplus with subsidy, producer

surplus with subsidy and total surplus with subsidy. Label your calculations. (40

points)

b.

Compare the value of the total surplus before the subsidy

and the value of the total surplus after the subsidy. Is the society better or

worse off with the subsidy? Explain. (14 points)

c.

Using total surplus before the subsidy and total

surplus after the subsidy calculate the deadweight loss created by the subsidy.

(6 points)

d.

With reference to marginal benefit and marginal cost

explain the deadweight loss created by the subsidy. (6 points)

e. Calculate

the per unit consumer share of the subsidy. (6 points)

A low income town decides to impose a $3 per unit subsidy on

the consumers of T-shirts. The supply and demand for T-shirts are described by

the following equations:

Supply: Q = 2P

Demand: Q = 20 - 2P

Q measures the quantity of T-shirts, and P measures the

price per T-shirt.

a.

Graphically illustrate the effect of this subsidy on the

T-shirt market and calculate the consumer surplus with subsidy, producer

surplus with subsidy and total surplus with subsidy. Label your calculations. (40

points)

b.

Compare the value of the total surplus before the subsidy

and the value of the total surplus after the subsidy. Is the society better or

worse off with the subsidy? Explain. (14 points)

c.

Using total surplus before the subsidy and total

surplus after the subsidy calculate the deadweight loss created by the subsidy.

(6 points)

d.

With reference to marginal benefit and marginal cost

explain the deadweight loss created by the subsidy. (6 points)

e. Calculate

the per unit consumer share of the

Answer 1

Answer;

a. Calculation of equilibrium price and quantity:

To calculate equilibrium price and quantity, we must equate demand function with supply function.

20 - 2P = 2P or 4P = 20 So P = 5

Plugging in the value of P in demand function to calculate Q,

Q = 20 - 2P or Q = 20 - 2*5 So Q = 10

The resulting graph and introduction of subsidy look like this:

Pp - @ TO 120 7 76

As a result of the subsidy, consumer surplus (CS) = area of a+b+d+g+f

Mathematically, it is the area of the triangle below equilibrium demand curve and Pc. So,

CS = ½ * (10 - 3.5) * 13 = ½ * 6.5 * 13 CS = $42.25

Producer surplus (PS) = area of b+c+d+g+h

Or, the area above the supply curve and below the Pp line.

PS = ½ * 6.5 * 13 PS = $42.25

total surplus = 42.25 + 42.25 = $84.50

b. Before the subsidy,

CS = ½ * 5 * 10 = $25

PS = ½ * 5 * 10 = $25

Total surplus = 25 + 25 = $50

Difference in CS = 42.25 - 25 = $17.25

Difference in PS = 42.25 - 25 = $17.25

Difference in Total surplus= 84.50 - 50 = $34.50

The society is better off with subsidy. The subsidy has led to increased consumer surplus and producer surplus, and thereby total surplus, indicating an increase in social welfare.

c. Total surplus before the subsidy = $50

Total surplus after the subsidy = $84.50

Difference = $4.5 (that is net increase in the surplus - subsidy amount or 34.50 - 30) is the deadweight loss. It is indicated in the graph as the area of the triangle e in orange.

deadweight loss = $4.5

d. Marginal benefit is the increase in consumer surplus because of subsidy. This increase in CS is indicated by area of d+g+f.

Marginal cost is the area of increased producer surplus, indicated by area of b+c.

The subsidy amount is the area of b+c+d+g+f+e, or CS + PS + triangle e.

So the area of triangle e goes neither to consumers not to producers. So,the area of triangle e is deadweight loss.

e. Per unit consumer share of the subsidy = change in CS/ Q = 17.25/ 13 = $1.33