2. The demand for Q is assumed to be deterministic, while the supply

of Q is subject to some random disturbances. Speci.cally, one may

write the demand function as Q = a P and the supply function

as Q = bj P; where a > 0 and bj > 0 (j = H;L): Given the

randomness in supply, we here assume that bj take only two possible

values: bj = bH and bj = bL with equal probability. Consider the

following two scenarios: case

(i) The government decides to let the

market determine the equilibrium price. In this case, consumers may

pay a high price (denoted as PH) when b = bL or a low price (denoted

as P L) when b = bH. They happen with equal probability; case

(ii) Thegovernment .gures out the mean supply, Q = bH+bL/2 - P and controls

the price at PH+PL/2 irrespective of the supply conditions. In this case,

the government acts as an agency to buy or sell whenever there exists

an excess supply or demand. Assume that there is no storage and

processing costs for the government to do so.

(a) Show graphically the expected consumer.s surplus (CS), producer.s

surplus (PS), and social welfare under case (i).

(b) Show graphically the expected consumer.s surplus (CS), producer.s

surplus (PS), and social welfare under case (ii).

(c) Compare the expected social welfare between case (i) and case

(ii). Is the country better or worse o. if the government decides

to choose (ii) over (i)? Your analysis should be as rigorous as

possible.

(d) What if the storage and processing costs are not zero ($c, say)?