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f07 ec51 ps3 answers

f07 ec51 ps3 answers - Economics 51D Due 17 September 2007...

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Economics 51D Due 17 September 2007 PROBLEM SET 3 ANSWERS 1. The Pinkies of Paramus? C. We’ll start with C first, since (hopefully) it’s obvious that the demand curve here is a linear function. But the function has Q as a function of P, whereas our supply n demand model has P on the vertical axis and Q on the horizontal axis—in other words, P as a function of Q. That’s easily changed, if we solve for P: P = 300 – Q / 50. So if we graph this on our usual Q-P space (with P on the vertical axis), then the y-intercept is 300 and the slope is – 1 / 50 or -.02. This makes sense since we think demand curves are downward sloping. A. The size of the market really asks what the maximum potential demand for the good is—we can find this from our demand curve by putting in 0 for P and seeing how many pinkie rings would be demanded if we effectively gave them away—15,000. B. The answer to Part C above helps us see what the maximum price is that the consumers are willing to pay. If we take the equation from Part A and insert Q = 0, then P = 300, or y-intercept. This actually says that if the price of pinkie rings rises to $300, demand vanishes so that $300 is effectively the maximum price that someone would pay (technically, it’s $299.99 or $300 – ε, but we’ll round to $300). Note that we’ve inferred a bunch of information very quickly and easily from this linear demand curve. They are easy to work with and have nice characteristics, like the maximum price and maximum market size. D. If the price of a pinkie ring is $195, then the quantity demanded, using the first demand curve Q = 15,000 – 50P, is 15,000 – 50*195 = 15,000 – 9,750 = 5,250 pinkie rings. Similarly, quantity demanded when price is $220 is given by 15,000 – 50*230 = 15,000 – 11,500 = 3,500. So the quantity demanded declines from 5,250 rings to 3,500 rings. E. This is given on the attached spreadsheet. F. This is also given on the spreadsheet. Note that the Total Revenue curve is for the market, not for an individual firm. Remember that an individual firm takes the price as given, so its total revenue would simply be a line through the origin with slope equal to the market price of pinkie rings. Nonetheless, it’s interesting to examine how price and quantity interact at the market level to produce the total revenue function for the market. As the graph shows, this function looks like a quadratic function, with a maximum at some intermediate price. G. Now we have a very different demand curve. As we did in Part C, let’s rewrite this function so that price is the y-axis variable: P = 900,000 / Q. Unlike the linear demand curve, there is no “maximum” price that consumers are willing to pay or any limit to the size of the market—if we
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put in P = 0, we get that Q is infinite, and if we put in Q = 0, then we get that P is infinite. This is a nonlinear demand curve—a rectangular hyperbola, to be exact. Let’s graph it and see. As the problem suggests, let the prices go from 1500 to 3000, and then infer the quantity demanded and the total revenues. This is given on the spreadsheet, along with the graph. The graph does look like a hyperbola.
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