Question 3.15: The demand and supply functions of a good (shirts) are given......
The demand and supply functions of a good (shirts) are given as
Demand function: P = 60 − 0.6Q
Supply function: P = 20 + 0.2Q
(a) Calculate the equilibrium price and quantity for shirts algebraically and graphically.
(b) Calculate the values of consumer and producer surplus at market equilibrium. Illustrate CS and PS on the graph in (a).
(c) What is the value of total surplus?
(a) The algebraic solution to this part is given over to the reader. Show that the equilibrium quantity and price of shirts are 50 units and £30, respectively. The graphical solution is the point E_0 illustrated in Figure 3.14.
(b) Consumer and producer surplus at market equilibrium are calculated as follows:
At P = 30, Q = 50 CS = triangle AP_0E_0 = 0.5 × 50 × 30 = 750
At P = 30, Q = 50 P S = triangle BP_0E_0 = 0.5 × 50 × 10 = 250
(c) Total surplus is the sum of consumer and producer surplus; therefore
TS = CS + P S = 750 + 250 = 1000
