Question

Suppose that the USDA expects that 53.3 billion bushels of soybeans will be produced this year at a price of $8.50/bushel. Assume that the elasticity of supply is 0.3 and that the elasticity of demand is -0.2 (both very inelastic).

1. Derive the linear supply and demand curves for this equilibrium.

2. What quota is required to increase the soybean price to $9.25/bushel? And what is the economic cost of this solution (i.e., what is the change in producer surplus and change in consumer surplus, and what is the sum of these changes)?

3. What is the economic cost of obtaining this price by creating a price floor of $9.25/bushel? How much subsidy is required for this equilibrium?

4. Could you argue that one approach is better than the other (should the government impose a quota versus creating a price floor)?

Answer 1

Answer 1

given easticity of suppy Es = 0.3

quantity demaded Qs = 53.3

price (P) = 8.50

at equilibrium Q_s= Q_d

E_s= 0.3

E_d= - 0.2

deriving suppy curve (linear) Q_s = c+ dP

easticity of supply E_s= d * P/Q

so, d = E_s / P/Q = Es * Q/P

i.e d =0.3* 53.3/8.50

calcuation gives d= 1.88

so linear suppy function

Qs = C + 1.88 P

C= Qs - dP

C= 53.3 - 1.88 (8.50) =37.32

i.e (37.32)

Qs= 37.32 + 1.88 P

simiary deriving inear demand function from given data

Qd = a - b P

elasticity of demand Ed = b*(P/Q)

b = -Ed / (P/Q)

= - Ed * Q / P

= - 0.2 * 53.3 / 8.5

= - 1.25

as Qd = a - b P

so a = Qd + b P

a = 53.3 + ( -1.25 *8.50)

a = 53.3 - 10.65

a = 42. 65

so Qd = a - bP

Qd = 42.65 - 1.25 P