The general linear demand for Di-lithium crystals is estimated to be:

Q = 125,000 - 400P - 0.76M + 360P_R

where P is the price of Di-lithium crystals (per microgram),

 M is average budget (treat like income) of ship engineers who buy Di-lithium crystals,

P_R is the price of related good R (Rhodium oxide).

The values of P, M, and P_R are expected to be $300 per microgram, $50,000, and $150, respectively.

Use these values at this point on the demand curve to make the following computations. 

[Hint: Remember that the slope parameter, b, measures the rate of change in quantity demanded per unit change in price (i.e., b = ΔQ/ΔP) in the general equation Q = a + bP + cY + dZ.  The same relationship holds for c (c = ΔQ/ΔY) and d (d= ΔQ/ΔZ).]

a. Compute the quantity of Di-lithium crystals demanded for the given values of P, M, and P_R.

b. For the quantity in part a, calculate the point price elasticity of demand. At this point on the demand curve, is demand elastic, inelastic, or unitary elastic?  How would decreasing the price of Di-lithium crystals affect total revenue? Explain.

c. Calculate the budget (income) elasticity of demand ε_M. Are Di-lithium crystals normal or inferior? Explain how a 3.5 percent decrease in budget (income) would affect demand for Di-lithium, all other factors affecting the demand for Di-lithium crystals remaining the same.

d. Calculate the cross-price elasticity ε_XR. Are the Di-lithium crystals and R substitutes or complements? Explain how a 6 percent increase in the price of related good R would affect demand for Di-lithium crystals, all other factors affecting the demand for Di-lithium crystals remaining the same?

e. Find the equations for demand (i.e., Q = a + bP), inverse demand (i.e., P = a + bQ) and marginal revenue for the given values of P, M, and P_R. At the point on the demand curve in parts a and b, is marginal revenue positive, negative or zero? Is this as you expected? Explain why or why not