Question

Suppose the demand and supply for black forest cake in Melbourne is represented by the following table.

Price ($/hour)	Quantity demanded (hours per day)	Quantity supplied (hours per day)
15.00	750	0
22.50	625	250
30.00	500	500
37.50	375	750
45.00	250	1000
52.50	125	1250
60.00	0	1500

1. Calculate the equilibrium price and quantity of black forest cake in Melbourne and sketch this on a clearly labeled diagram. (You can assume the curves are linear all the way to the axes.)  
2. Calculate the consumer and producer surplus and show them on your diagram.

Suppose the government wants to try to decrease the quantity of cakes due to the high quantity of sugar used. The government, therefore, imposes a per-unit tax of $22.50 on all desserts made with added sugar.

3. What will be the new quantity of black forest cake purchased, what will be the price the consumers pay, and what price will bakers receive?  Show this on your diagram.
4. Calculate the tax burden for consumers and for producers and show this on your diagram.
5. Calculate the deadweight loss of this tax and show this on your diagram. (1 mark)
6. Use a diagram to help explain the likely effects of this tax on the market for fruit salad (1 mark)

Answer 1

A. Refer the attached picture below the equilibrium price is $ 30 / hour and quantity is 500 hours per day.

B. Consumer surplus = (1/2)×(60 - 30)×500 = $ 7,500

Producer surplus =(1/2)×(30 -15)×500 = $ 3,750

Now a tax of $ 22.50 per unit is imposed then the equilibrium quantity will change as well as price.

The inverse demand function is P = 60 - 0.06Q_D

Q = 1000 - (50/3)P

Supply function is, P = 15 + 0.03Qs

Due to tax the supply. Curve will change

P - 22.5 = 15 + 0.03Qs

P = 37.5 + 0.03Qs

Qs = (100/3)P - 1250

Now equate the demand function and the new supply equation we get

1000 -(50/3)P = (100/3)P - 1250

(100/3)P + (50/3)P = 1000 + 1250

(150/3)P = 2250

50P = 2250

P = $ 45 / hour

Q = 1000 -(100/6)×45 = 250 units

Quantity purchased = 250

Price buyers pay = $ 45

Price sellers receive = $ 22.5

D. Tax burden on consumer = 15*250 = $ 3,750

Tax burden on sellers = (30-22.5)×250 = $ 1,875

E. Deadweight loss =(1/2)×(45-22.5)×(500-250) = $ 2,812.50

F. Due to this tax burden the consumers will switch to fruit salad. Thus, the demand curve of fruit salad will shift to its right.

Please contact if having any query will be obliged to you for your generous support. Please help me it mean a lot to me. Thank you.