Please show all step by step with graph(s)

1st part

Imagine that you have been given a job as an economic advisor to evaluate a certain competitive US manufacturing industry. Your (accurate) statistical analysis indicates the market is characterized by demand of Q_d = 500 - 8P and supply of Q_s = 4P - 100.

• Solve for equilibrium price P₁ and quantity Q₁.
• Depict the supply curve S₁ and demand curve D₁ on the usual P, Q diagram. Label all intercepts (including two intercepts for the demand curve and one intercept for the supply curve). Clearly indicate and label the market equilibrium.
• Graphically indicate the areas of Consumer Surplus (CS₁) and Producer Surplus (PS₁).
• Compute the values of Consumer Surplus (CS₁) and Producer Surplus (PS₁), clearly indicating the units that CS and PS are measured in.

2nd part

Continuing your analysis of the competitive US manufacturing industry from Question 1, with demand of Q_d = 500 - 8P and supply of Q_s = 4P - 100, suppose a technological innovation causes the supply curve to increase, shifting the curve down by $15 for every given quantity Q.

• Determine the new supply equation.
• Solve for equilibrium price P₂ and quantity Q₂.
• Depict the original supply S₁, the new supply S₂, and the original demand D₁on the usual P, Q diagram. Label all intercepts (including two intercepts for the demand curve and one intercept for the supply curve). Clearly indicate and label the new market equilibrium.
• Graphically indicate the areas of Consumer Surplus (CS₂) and Producer Surplus (PS₂) that resulted from the new market equilibrium.
• Compute the values of Consumer Surplus (CS₂) and Producer Surplus (PS₂) associated with the new market equilibrium, clearly indicating the units that CS and PS are measured in.
• Who has benefited from technological innovation, based on the comparison of CS and PS in Questions 1 and 2? Consumers, producers, or both? Why? (Narrative response; suggested length of three to four sentences or one paragraph.)