The generalized demand and supply functions for good x

Question

Question: Stuck on these questions. Need help solving with explanation so I can understand.

Question 1:

The generalized demand and supply functions for good X are:

Qd = 10 - 2Px + 2P_Y  +M

Qs = 10 + 2P_X

a) What is the demand function when P_Y = $2 and M = $500?

b) Use the demand function you found in part a. and solve for the equilibrium price (P_o) and the equilibrium quantity (Q_o).

c) Find the inverse demand function and the inverse supply function.

d) Sketch this market and identify consumers and producers surpluses areas.

Question 2:

A firm hires a consultant to estimate the demand function for its product. Using regression analysis, the consultant estimates the demand function to be log Q = 2.01 - 0.148 log P + 0.258 log Z where Q is the quantity demanded (in tons) of Delta's product, P is the price (in dollars per ton) of Delta's product, and Z is the price (in dollars per ton) of a rival product.

a. Calculate the price elasticity of demand for Delta's product.

b. Calculate the cross elasticity of demand between Delta's product and the rival product.

c. According to the consultant, R2 = 0.98 and the standard error of estimate is 0.001. If the number of observations is 94, comment on the goodness of fit of the regression.