Question

(Please explain steps and logic behind them)

Exercise 3: Supply

At the current market equilibrium, the price of a good equals $40 and the quantity equals 10 units. At this equilibrium, the price elasticity of supply is 2.0. Assume that the supply curve is linear.

(a)Use the price elasticity and market equilibrium to find the supply curve.

(b)Calculate the producer surplus in the market.

(c)Imagine that a policy results in the price falling from $40 to $30. By how much does producer surplus fall?

(d)What fraction of the lost producer surplus is due to the reduction in the quantity supplied and what fraction is due to the fall in price received per unit sold?

Answer 1

(a) Es = 2; P = 40; Q = 10
Now, Es = (Change in Q/Change in P)*P/Q = 2
So, (Change in Q/Change in P)*(40/10) = 2
So, (Change in Q/Change in P)*4 = 2
So, (Change in Q/Change in P) = 2/4 = 0.5

Supply curve is given by Q = a + bP
where b = Change in Q/Change in P = 0.5
At Q = 10; P = 40;
10 = a + 0.5P = a + 0.5(40) = a + 20
So, a = 10 - 20 = -10

So, Q = -10 + 0.5P

(b) When Q = 0 = -10 + 0.5P
So, 0.5P = 10
So, P = 10/0.5
So, minimum P, Pmin = 20

PS = area of triangle = (1/2)*base*height = (1/2)*Q*(P-Pmin) = (1/2)*10*(40-20) = 5*20 = $100

(c) At P' = 30; Q' = -10 + 0.5(30) = -10 + 15 = 5
Fall in PS = area of trapezium = [(Q+Q')/2]*(P-P') = [(10+5)/2]*(40-30) = (15/2)*10 = $75

(d) Lost surplus due to decrease in quantity supplied = area of triangle = (1/2)*(Q-Q')*(P-P') = (1/2)*(10-5)*(40-30) = (1/2)*5*10 = $25
So, fraction of loss surplus due to decrease in quantity = 25/75 = 1/3
Thus, fraction of loss surplus due to decrease in price = 1 - (1/3) = 2/3