1. The general linear demand for good X is estimated to be

Q = 125,000 - 200P +1.2M + 300P_R

Where P is the price of good X, M is the average income of consumers who buy good X and P_R is the price of related good R. The current values of M and P_R are expected to be $40,000 and $150, respectively. 

a. Write the direct demand function in the form Q = a + bP

b. Write the inverse demand function in the form P = A + BQ

c. Write the equation for marginal revenue and calculate the quantity and price where total revenue is maximized.

d. If P is instead set at $200, calculate the quantity of good X demanded and calculate the point price elasticity of demand at this price and quantity.

e. At this point from part d), is demand elastic, inelastic or unitary elastic? Is marginal revenue positive or negative at this point?

f. Calculate the income elasticity of demand for this good at the point from part d). Is good X normal or inferior?

g. Calculate the effect of a 3.5 percent decrease in income on the demand for good X (all other demand factors being held constant and price =$200).