Question

. (9 points) The daily market for cups of chai tea at Jeff’s Espresso is given by the following supply and demand equations.

QD =160−20P QS = 20P

Please answer the following questions about this market:

a. Draw the supply and demand curves below. Be sure to label the y-intercepts of each graph and the equilibrium and label the supply curve S. Solve for the equilibrium price and quantity in this market.

b. What is the consumer surplus in this market? What’s the producer surplus in this market?

c. Now imagine that the city imposes a $0.50 per cup tax on all hot drinks. This changes the equation of the supply curve to

QS = 20P − 10
Draw this new supply curve on the graph, label it S2. Calculate the new equilibrium price and

quantity in the market. What is the deadweight loss of the tax?

Answer 1

Answer

The demand equation and supply equation of cups of tea at Jeff’s Espresso are as follows;

Demand equation: QD =160 −20P................(1)

Supply equation: QS = 20P......................(2)

a. Let us form a table of quantity demanded and quantity supplied of tea at Jeff’s Espresso for some price levels below;

Table-1

Price($)	QD(cups of tea)	QS(cups of tea)
0	160	0
2	120	40
4	80	80
6	40	120
8	0	160

The demand curve, supply curve , and equilibrium price and quantity in this market are shown in the figure below;

In the above figure, the curve 'DD' is the demand curve of tea, and the curve 'SS' is the supply curve of tea. The point 'E' shows the equilibrium point in this market. The equilibrium price is $4, and the equilibrium quantity is 80 cups of tea.

Price 10 Demand and Supply Curves of Tea 8 0,8 160,8 40,6 120,6 80,4 40,2 120,2 0,0 160,0 40 80 120 160 200 Quantity

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b.  Consumer surplus in this market is $160 ; Producer surplus in this market is $160.The green triangle in the above figure shows the consumer surplus(CS) in this market. The blue triangle in the above figure shows the producer surplus(PS) in this market.

Price 10 Demand and Supply Curves of Tea 8 0,8 160,8 -40,6 120,6 80,4 40.2 120,2 0,0 160,0 40 80 120 160 200 Quantity

CS = 1/2 * base * height

Or, CS = 1/2 * (80 ) * ($8 - $4)

Or, CS = 40 * ($4)

Or, CS = $160

The consumer surplus in this market is $160.

PS = 1/2 * base * height

Or, PS = 1/2 * 80 * ($4 - $0)

Or, PS = 40 * ($4)

Or, PS = $160

The producer surplus in this market is $160.

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c. The city imposes a $0.50 per cup tax on all hot drinks. This changes the equation of the supply curve to

QS = 20P − 10......(2^')

The quantity demanded is unchanged, and thus the demand equation remains same as before,

QD =160 −20P

At the equilibrium condition,

QD = QS

$\therefore$  160 −20P = 20P − 10

Or, − 20P - 20P = -10 - 160

Or, - 40P = -170

Or, P = -170 / -40

Or, P = 4.25

Putting the value of P in equation 2, we get,

QS = 20 * (4.25) − 10

Or, QS = 85 - 10

Or, QS = 75

Now, let us see the quantity demanded at this price,

QD =160 −20 * (4.25)

Or, QD =160 − 85

Or, QD = 75

Thus, QD = QS = 75

So, the new equilibrium price is $4.25, and the equilibrium quantity is 75 cups of tea.

Let us find the quantity supplied after the imposition of tax, and form a new table, Table-2, with the existing price level and quantity demanded as in Table-1.

Table-2

Price($)	QD(cups of tea)	QS(cups of tea)
0	160	-10
2	120	30
4	80	70
6	40	110
8	0	150

In the above figure, 'S₁' is the new supply curve of tea. The new equilibrium point is attained at point 'A'., where equilibrium price the consumer pays is $4.25 ,and the equilibrium quantity is 75 cups pf tea.

Demand and Supply Curves of Tea PACE -40 40 80 120 160 200 Quantity

The deadweight loss (DWL) of tax is shown by the area of the triangle $\Delta$ AET

After the tax, the supply curve shifts leftward by the amount of tax, $0.50, and the equilibrium quantity decreases from 80 cups to 75 cups of tea.With the increase of equilibrium price, and decrease of equilibrium quantity, there arises DWL.

Let us now calculate the DWL = Area of triangle $\Delta$ AET

Area of triangle $\Delta$ AET = 1/2 * base * height ; where base = decrease of quantity, and height = amount of tax.

DWL = 1/2 * (80 -75) * ($0.50)

Or, DWL = 1/2 * 5 * ($0.5)

Or, DWL = 2.5 * ($0.5)

Or, DWL = $1.25

Thus, the deadweight loss of the tax is $1.25.

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