The market demand and supply functions for potatoes are:QD = 2,000 - 500P and QS = 800 + 100P.To help potato producers, the government is considering legislation that would put a pricefloor at R2.25 per bag. If this price floor is implemented, determine (i) how many bags ofpotatoes will the government be forced to buy to keep the price at R2.25; (ii) how muchgovernment will spend in total; and (iii) how much producer- and consumer -surplus changes

(i) To determine how many bags of potatoes the government will be forced to buy to keep the price at R2.25, we first need to find out the quantity demanded (QD) and the quantity supplied (QS) at this price.

The quantity demanded at price R2.25 can be found by substituting P = 2.25 into the demand function:

QD = 2000 - 500*2.25 = 2000 - 1125 = 875 bags

The quantity supplied at price R2.25 can be found by substituting P = 2.25 into the supply function:

QS = 800 + 100*2.25 = 800 + 225 = 1025 bags

The government will have to buy the excess supply, which is the difference between the quantity supplied and the quantity demanded:

Excess supply = QS - QD = 1025 - 875 = 150 bags

(ii) The total amount the government will spend can be found by multiplying the price per bag by the number of bags:

Total expenditure = Price per bag * Number of bags = R2.25 * 150 = R337.5

(iii) The change in producer surplus is the difference between the revenue from selling at the price floor and the revenue from selling at the equilibrium price. The equilibrium price is where the quantity demanded equals the quantity supplied. Setting QD = QS, we get:

2000 - 500P = 800 + 100P 600P = 1200 P = 2

The equilibrium quantity is Q = 2000 - 500*2 = 1000 bags

The revenue at the equilibrium price is R2 * 1000 = R2000

The revenue at the price floor is R2.25 * 1025 = R2306.25

So the change in producer surplus is R2306.25 - R2000 = R306.25

The change in consumer surplus is the difference between the amount consumers are willing to pay at the equilibrium price and the amount they actually pay at the price floor. The amount consumers are willing to pay at the equilibrium price is the area under the demand curve up to the equilibrium quantity, which is (1/2) * 1000 * 2 = R1000. The amount they actually pay at the price floor is R2.25 * 875 = R1968.75. So the change in consumer surplus is R1000 - R1968.75 = -R968.75. The negative sign indicates a loss in consumer surplus.