Question 3.13: The demand and supply functions for a good (£P per ton of po......
The demand and supply functions for a good (£P per ton of potatoes) are given as
Demand function: P_d = 450 − 2Q_d (3.20)
Supply function: P_s = 100 + 5Q_s (3.21)
(a) Calculate the equilibrium price and quantity.
(b) The government provides a subsidy of £70 per unit (ton) sold:
(i) Write down the equation of the supply function, adjusted for the subsidy.
(ii) Find the new equilibrium price and quantity algebraically and graphically.
(iii) Outline the distribution of the subsidy, that is, calculate how much of the subsidy is received by the consumer and the supplier.
(a) The solution to this part is given over to the reader. Show that the equilibrium quantity and price are 50 units and £350, respectively.
(b) (i) With a subsidy of £70 per unit sold, the producer receives (P_s + 70). The equation of the supply function adjusted for subsidy is
P_s + 70 = 100 + 5Q
P_s = 30 + 5Q (3.22)
The supply function is translated vertically downwards by 70 units. This is illustrated in Figure 3.9 as a line parallel to the original supply function.
(ii) The new equilibrium price and quantity are calculated by equating the original demand function, equation (3.20), and the supply function adjusted for the subsidy, equation (3.22):
P_d = (P_s + \text{subsidy})
450 − 2Q = 30 + 5Q equating equations (3.20) and (3.22)
Q = 60
Substitute the new equilibrium quantity Q=60 into either equation (3.20) or equation (3.22) and solve for the new equilibrium price:
P = 450 − 2Q
P = 450 − 2(60) substituting Q = 60 into equation (3.20)
P = 330
The point (P = 330, Q = 60) is shown as point E_1 in Figure 3.9
(iii) The consumer always pays the equilibrium price, therefore, the consumer pays £330, a decrease of £20 on the equilibrium price with no subsidy (£350). This means that the consumer receives 20/70 of the subsidy. The producer receives the equilibrium price, plus the subsidy, so the producer receives £330 + £70 = £400, an increase of £50 on the original price of £350. The producer receives 50/70 of the subsidy.
In this case, the subsidy is not evenly distributed between the consumer and producer; the producer receives a greater fraction of the subsidy than the consumer. The reason? The slope of the supply function is greater than the slope of the demand function (ignoring signs).
