Determine the demand function and inverse demand function

Question

1. The demand for good X is given by: Q_X^d = 6,000 - ½ P_X - P_Y + 9P_Z + 1/10M Research shows that the prices of related goods are given by P_Y = $6,500 and P_Z = $100, while the average income of the individuals consuming this product is M = $70,000.

a. Indicate whether goods Y and Z are substitutes or complements for good X.

b. Is X an inferior good or normal good?

c. How many units of good X will be purchased when P_X = $5,230?

d. Determine the demand function and inverse demand function for good X. Graph the demand curve for good X.

2.The demand curve for product x is given by Q_X^d= 300 - 2P_X

a.) Find the inverse demand curve.

b.) How much consumer surplus do consumers receive when P_X=$45?

c.) How much consumer surplus do consumers receive when P_X=$30?

d.) In general, to the level of consumer surplus as the price as the price of a good falls?