C2 Nov 2000 #52

[Avi]

Why when the cap is placed at 3, do we use the Demand equation to determine amount produced? Since when is a monopolist producing at the demand as long as there is no optimal two-part tarriff? What changes from using the MR curve to the Q_D curve?

--Avi

[Gandalf]

I can't answer in the terms you're using, but here's what's happening.

Monopolist wants to maximize its profit = Revenue - Costs = (8y - 4y^2) - (.5+2y) = 6y-4y^2-.5

Without constraints, you can get the maximum by setting dProfit / dy = 0; that's the same as saying Marginal Revenue = Marginal Cost.

With constraints, Revenue = 3y for y <= 1.25 (the most you can charge is 3, and you will sell them all; people would be willing to pay more than 3).

Profit = 3y - (.5 + 2y) = y - .5, for y < 1.25. That's an increasing function of y, produce as many as you can up to the 1.25 point where the Profit function is different.

At 1.25, profit function reverts to 6y - 4y^2 -.5. Derivative would be negative; don't produce any more.

I don't think you could do all that within exam time constraints, but maybe it will help you understand the study material.

[Avi]

Thank you, the theoretical underpinnings always help to elucidate the material

--Avi