Question

The demand for sandwiches is given by QD = −2P + 70, while supply is given by QS = 5P.

• Calculate the equilibrium price and quantity of sandwiches.

• Suppose there are problems with delivery of the necessary production inputs, and as a result, the output was limited do 30 sandwiches. At what price is the demand equal to 30? How many sandwiches would supplier ideally provide at this price?

• Suppose now there are no problems with production. How many sandwiches will be supplied if the government provides a subsidy of 7 to every sandwich? • Use a supply and demand graph to discuss how will the market equilibrium change if the consumers suddenly lose their taste for sandwiches.

Answer 1

(1) In equilibrium, QD = QS

- 2P + 70 = 5P

7P = 70

P = 10

Q = 5 x 10 = 50

(2) When QS = 30,

From demand function: 30 = - 2P + 70

2P = 40

P = 20 (demand price)

From supply function: When P = 20,

QS = 5 x 20 = 100

(3) The subsidy will shift supply curve rightward by $7 at every output level and new supply function is

QS = 5 x (P + 7) = 5P + 35

Equating with QD,

- 2P + 70 = 5P + 35

7P = 35

P = 7 (Price paid by buyers, which is market price)

Price received by sellers = 7 + 7 = 14

Q = 5 x 7 + 35 = 35 + 35 = 70

(4) A negative taste preference will decrease demand for the good, so its demand curve will shift leftward, decreasing both price and quantity.

In following graph, D0 and S0 are initial demand and supply curves intersecting at point A with equilibrium price P0 and quantity Q0. When demand falls, D0 shifts left to D1, intersecting S0 at point B with lower price P1 and lower quantity Q1.

3 9.