Question

Assume candy hearts is a generic product sold in a perfectly competitive market. The demand for candy hearts in February is estimated to be

Qd = 160 – 8P                  or                     P = 20 – (1/8)Qd

and the supply of candy hearts in February is estimated to be

Qs = 70 + 7P                    or                     P = -10 + (1/7)Qs

where P is the dollar price of a 6-pack of candy hearts, and Qd and Qs represent the monthly quantity demanded and supplied (respectively) of 6-packs. Quantities are measured in thousands of 6-packs. Show all your work in answering the following questions.

1) Assume this is a perfectly competitive market, and compute the equilibrium price and quantity of candy hearts.

2) Draw a diagram of the demand and supply curves. Indicate the equilibrium price and quantity and label the coordinates of the equilibrium point on the axes. ALSO, indicate the numerical values of: the price-axis intercept of the demand curve (i.e. the price at which the quantity demanded is 0), the quantity-axis intercept of the demand curve (i.e. the quantity demanded if the price is $0), and the price-axis intercept of the supply curve (the price at which the quantity supplied is 0).

3) To make candy hearts more affordable, on February 1, the government votes to institute a price ceiling of $3 on candy hearts. Will this affect the amount of candy hearts traded? Explain the impact, if any, on quantity demanded, quantity supplied, and the quantity traded.

4) Give a brief definition of “deadweight loss” and compute the deadweight loss (in dollars) of the price ceiling of $3 in this market in February. Remember, quantity is measured in thousands of 6-packs.

5) Who benefits from the $3 price ceiling? Who is negatively impacted by the $3 price ceiling? Explain carefully.

Answer 1

1) Assume this is a perfectly competitive market, the equilibrium price and quantity of candy hearts is found by equating demand and supply

160 – 8P = 70 + 7P

90 = 15P

P = $6 per pack and quantity = 70 + 7*6 = 112 (thousand) packs.

2) The diagram of the demand and supply curves is shown below.

3) Now the government votes to institute a price ceiling of $3 on candy hearts. This will create a shortage of candy hearts because at the ceiling price, the quantity demanded is 160 – 8*3 = 136 (thousand) packs and quantity supplied is 70 + 7*3 = 91 (thousand) packs. Hence there is a shortage of 136 – 91 = 45 thousand packs. The quantity traded is 91 thousand packs

4) Deadweight loss is the societal loss that occurs due to market distortions. When the market is not able to allocate resources efficiently, the result is a loss in the efficiency measured by the deadweight loss. Here DWL = 0.5*(8.625 - 3)*91000 = 255937.50

5) Producer benefit from the $3 price ceiling because the producer surplus is increased. Consumers are at a loss because their surplus has fallen.