Final answer:
A price floor of $12 in the market for good X will result in a surplus of 18 units, as the quantity supplied exceeds the quantity demanded. The producer's surplus and consumer's surplus cannot be precisely calculated without the specific numerical values associated with the graph provided.
Step-by-step explanation:
The student is asking about the effects of government interventions in the form of price controls, specifically a price floor in the market for a good X. The demand function given is x = 90 − 3P and the supply function is x = 6P. At a price floor of $12, we must first identify if there will be a shortage or surplus.
a) To determine whether there will be a shortage or surplus, we must calculate the quantity demanded and supplied at the price floor. At a price of $12, the quantity demanded would be x = 90 − 3(12) = 54, and the quantity supplied would be x = 6(12) = 72. Since more units are supplied than demanded, there will be a surplus.
b) The surplus can be determined by subtracting the quantity demanded from the quantity supplied: 72 − 54 = 18 units of surplus.
c) The producer's surplus is represented by the area above the supply curve and below the price floor, up to the quantity supplied. It can be calculated as the difference in price between the equilibrium price and the price floor, multiplied by the quantity supplied, plus the original producer surplus. Without the specific values of the areas labeled V, W, and X from the graph, we cannot calculate an exact numerical value.
d) The consumer's surplus is represented by the area below the demand curve and above the price. At a price floor of $12, this would be the area G from the illustration provided, as it is below the demand curve and above the price of $12. Without exact numerical values of the areas, a precise calculation cannot be made.