Final answer:
To find the new equilibrium quantity with a subsidy and a tax, adjust the supply and demand equations and set them equal to each other, resulting in Q=46. Calculating the deadweight loss requires further information such as elasticities or graphical analysis.
Step-by-step explanation:
To solve for the resulting quantity and the resulting deadweight loss with a given demand curve (P=132−Q) and supply curve (P=6+2Q), considering a subsidy of 24 and a tax of 12, we need to adjust the original supply and demand equations to account for the subsidy and tax.
First, the subsidy effectively lowers the cost of production, which means producers are willing to supply more at each price point. This shifts the supply curve downward by the subsidy amount. The new supply equation, including the subsidy, will be P = 6 + 2Q - subsidy. Therefore, P = 6 + 2Q - 24, or P = -18 + 2Q once we incorporate the subsidy.
Similarly, the tax increases the price paid by consumers, decreasing their demand. Hence, the demand curve shifts to the left by the tax amount. The new demand equation, including the tax, will be P = 132 - Q - tax. Therefore, P = 132 - Q - 12, or P = 120 - Q after including the tax.
To find the new equilibrium, set the adjusted demand curve equal to the adjusted supply curve and solve for Q:
120 - Q = -18 + 2Q
This results in 3Q = 138, therefore Q = 46.
The deadweight loss can then be determined by calculating the loss in consumer and producer surplus due to the market distortion created by the subsidy and tax. However, to calculate the exact deadweight loss, we would need additional information such as the elasticities of demand and supply, or we would conduct graphical analysis to visualize the changes in consumer and producer surplus.