Please help giving explanations, step, and mentioning specific functions or theorems used for each of the answers.

1) Given the following consumption C=a+bY where C is aggregated consumption and Y is national income and a>0 and 0

• What are the marginal function and average functions?
• What would be the income elasticity of consumption if national income were strictly positive?
• Would this consumption function be elastic or inelastic at positive national income levels? Explain why.

2) If the supply of a good is given by the following function Q=a+bP² + H^1/2 where Q is supply, P is price, H the size of harvest, and a<0 and b>0

• What is the price elasticity of supply, E_QP?
• What is the elasticity of supply given harvest, E_QH?

3) Given the demand function Q_D = D(P,Y₀) (D_P<0, >0) and supply function Q_S = S(P, T₀) (S_P>0, S_T0 <0) where T is tax and Y is income, and all derivatives are known to be continuous:

• What is the equilibrium condition? Write it as one equation.
• Explain why or why not the implicit function theory applies? If it does apply, what is the equilibrium identity?
• What are P/Yand P/Tat equilibrium price? What do they represent economically?
• Using the demand function what is Q/T?
• Using the supply function what is Q/Y?
• Explain why we must use the demand function in the first scenario and supply in the second?

4) Assume the demand and supply functions have changed and are now given by:

Q_D= D(P,C₀) (D/P<0,D/C>0) where C is consumer preference for a good and Qs=Qs₀. Assuming both partial derivatives are continuous:

• What is the equilibrium condition as a single equation? Show each step.
• How would equilibrium price vary with preference?
• Does the implicit function theorem apply? Why or why not?