# 455

1. The demand (marginal benefit) curve for pizza slices per month for a small city is as show in the graph below page. Its **inverse**can be described algebraically as: P= 4 – Q/2) (where P=price and Q=quantity in thousands of slices).

[Side Note: we call this the **inverse demand curve,**because the true demand curve says that quantity is a function of price, and that is because consumers are price takers. In other words, we consumers observe prices and then decide how much of a good to consume. In this case the true demand curve is Q = 8 – 2P. (Notice how we consume less at higher prices.) However, to make this an algebraic function where the amount on the Y axis (Price) is a function of the amount on the X axis (Quantity), we **invert**the demand curve. Algebraically, we do that by adding 2P to both sides, subtracting Q from both sides, and then dividing through by 2. (Check that out for yourself.) We also call this a “marginal benefit” or MB curve as it describes the marginal or additional or incremental benefit a consumer obtains from consumption of one more unit (Q) consumed.]

a. Add the following supply curve to the graph: P= 1 + Q/4. [Note that this equation describes and *inverse*supply relationship. The regular supply curve would be Q = 4P – 4. But you will deal with the inverse curves here. This is also called the “marginal cost” or MC curve because it describes the incremental cost of producing one more unit.]

[Hint: remember this trick from algebra to get you going on drawing the MC curve: ask yourself what “P” would be when “Q” is zero. That’s your “y intercept”, or in this case, your “P” intercept, since our Y axis is where we put price. Then ask where the line goes from there, which you can figure out by plugging in Q=1, or Q=2, etc. It’s a straight line, so you only need to do the calculation for two “Qs”. “Q=0” is the easiest, of course.]

Please label the curves (or as in the case here, straight lines) with “MB” (your inverse demand curve) and “MC” (your inverse supply curve).

b. What are the “market-clearing” or “equilibrium” quantity and price for pizza slices? We’re going to call these Qmand Pmwith the “m” being for “market”. [Big hint: Markets clear when consumers and producers agree on a price, and that leads to an agreement on the quantity that will be produced and purchased. Also note the scale of the X (or Q) axis – it is THOUSANDS of slices. This will affect your later $ values as well, but you should be sure to do that conversion in your answer about Qm.]

Qm=___

Pm=___

Please use the graph to help determine these quantities. Mark the point on the X and Y axis, respectively, with Qmand Pm.

Now please show how to determine these same quantities (Qmand Pm) using algebra.

Please put your algebra here and remember that your conclusions will be equations that say “Qm= [something]” and “Pm=[something]”.

c. What is the net [social] benefit at this optimal level of pizza slices? Your answer will be expressed as a number of dollars. Please shade an area in your graph that corresponds to this NET benefit.

To get the number of dollars, you may interpolate the relevant figures for your graph and then calculate the amount, or you can use algebra to get those figures.

[Hint: Net benefit for each slice of pizza is the excess of what consumers are willing to pay for the slice (otherwise known as their marginal benefit) over the cost of producing it (otherwise known as the marginal cost, or the supply curve). You are looking for the area of a triangle that has two parts: Consumer Surplus, and Producer Surplus.]

[Calculations here, if you go the algebra route.]

d. What if government requires pizza makers to charge $3/slice? How many slices will be sold, and what will be the net social benefit?

e. How does this change affect consumers, and how does it affect producers?

[Hint: We will use “consumer surplus” (CS) and “producer surplus” (PS) to make such comparisons. CS the areas between the demand curve and the price line. PS is the area between the price line and the supply curve. (Together they make up the net benefit you calculated in part d (for the optimal case) and part e (for the case with the price restriction). So you can answer the question by calculating* the change in CS and the change in PS due to the price restriction. *You can also look at areas on the graph that represent pre- and post-change CS and PS and eyeball whether each (or either) is bigger (or smaller) after the change. I am more interested in your qualitative answer than I am in the dollar figures involved.]

f. Another important quantity is the “Deadweight loss” associated with this policy.

Deadweight loss (DWL) is the cost to society of being stuck at a price-and-quantity combination that is different than the socially optimal combination.

DWL is typically a TRIANGLE, and if you think about the triangle as an arrowhead, the tip of the arrowhead will always point to the social optimum.

So, please shade and label the DWL triangle on your graph.

How many dollars does the DWL area represent? [Remember, the area of a triangle is “one half the base times the height”. Turn your head (or your paper) 90 degrees to turn the key vertical line into the “base” of that triangle (i.e. the base will be a difference you can measure on the Price/Y axis. The height will be a quantity you can measure along the Quanity/X axis.]

g. Assuming that the pizza pricing policy is not entirely arbitrary, what possible justification for it might you suggest? That is, why would the government agency even want to have such a policy?

Attachments:

ENVM650-ProbS….docx