DOC PREVIEW
Berkeley COMPSCI 294 - Economics tutorial

This preview shows page 1-2-20-21 out of 21 pages.

Save
View full document
View full document
Premium Document
Do you want full access? Go Premium and unlock all 21 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 21 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 21 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 21 pages.
Access to all documents
Download any document
Ad free experience
Premium Document
Do you want full access? Go Premium and unlock all 21 pages.
Access to all documents
Download any document
Ad free experience

Unformatted text preview:

Copyright 1997, David G. Messerschmitt. All rights reserved.Here we give a quick tutorial on the economics material that has been covered in class.For further information, the bookHal Varian, Intermediate Economics, A Modern Approach. New York, Norton, Fourth Edition, 1996.is recommended. If you are willing to purchase the book, I am sure one of the instructors will be pleased!Copyright 1997, David G. Messerschmitt 3/5/97 1Economics tutorialEconomics tutorialDavid G. MesserschmittDavid G. MesserschmittCS 294-6, EE 290X, BA 296.5CS 294-6, EE 290X, BA 296.5Copyright 1997, David G. Messerschmitt. All rights reserved.A “consumption bundle” is a particular quantity (x,y) of widgets and what’sits.It is convenient to define a utility function u(x,y), with the interpretation that a consumption bundle (x,y) with a higher utility is preferred to one with a smaller utility. No particular significance is attached to the numerical value of u(x,y), it simply defines an ordering relationship of conumption bundles which we interpret as consumer preference. That is, we do not interpret a doubling of utility as a doubling of preference, or a doubling of acceptable price, or anything like that. The utility function is thus not unique; for example the square root of the utility function or the logarithm of the utility functions represent exactly the same consumer preference.The indifference curve is defined asu(x,y) = constantwhere the constant is presumed to increase as we move toward larger consumption bundles. A larger constant represents a larger preference.We have shown the case where the indifference curves are convex, which means that the weighted average of two consumption bundles is preferred to either of the bundles alone. This is typical, but not necessary. (For example, either ice cream or olives alone would likely be preferred to their mixture.)Copyright 1997, David G. Messerschmitt 3/5/97 2Consumer preferencesConsumer preferencesQuantity ofwhat’sits yQuantity ofwidgets xConsumer is indifferent to any“consumption bundle” (x,y) on this curveIncreasing preferenceCopyright 1997, David G. Messerschmitt. All rights reserved.Instead of letting the vertical axis y be the quantity of what’sits consumed, let it be the total dollars spent on goods other than widgets.Presume that the price charged per unit of widget is p, and the consumer’s total income ($ available to spend on all goods) is m. Then we must have thatm = y + p*xThis is called the consumer’s budget line. The y-intercept of this line is m, and the slope is the negative of p.At the consumption bundle that maximizes the consumer’s utility and also falls on the budget line, the budget line will be tangent to an indifference curve.For the case shown, as is typical, the quantity of widgets consumed x will increase (move to the right) as the income m increases.Copyright 1997, David G. Messerschmitt 3/5/97 3Budget lineBudget line$ spent on allother goods yQuantity ofwidgets xIncomeSlope is negativeof price charged per unitof widgetConsumer preference ismaximizedCopyright 1997, David G. Messerschmitt. All rights reserved.Quasilinear preferences is a special case of a utility function for whichu(x,y) = v(x) + yThat is, the consumer’s utility increases linearly with y (the $ available to spend on all other goods).The indifference curve is given byu(x,y) = constant or y = constant - v(x)Thus, the indifference curves all have the same shape v(x) and are just vertically shifted versions of one another. For this special case, the optimum consumption bundle has a very special property: The consumption of widgets, x, does not depend on income m for any fixed price p. (This is because the slope of the indifference curve will equal p at a value of x that is independent of m.) Thus, this case models the situation where your consumption of widgets doesn’t depend on your income. This is probably a pretty good assumption for pencil widgets, and a bad assumption for BMW widgets.For this special case, we can easily find the price vs. quantity that the consumer will buy at that price. Substituting for the budget line, the utility isu(x,y) = v(x) + m - pxTaking the derivative and setting to zero, a condition for maximizing utility isv’(x) - p = 0 or p(x) = v’(x)p(x) vs. x is called the inverse demand function.Copyright 1997, David G. Messerschmitt 3/5/97 4Quasilinear prefrencesQuasilinear prefrences$ spent on allother goods yQuantity ofwidgets xSpecial case: indifference curvesare vertical shifts of one anotherConsumption of widgetsdoes not depend on incomeCopyright 1997, David G. Messerschmitt. All rights reserved.For the quasilinear consumer preference utility function, we saw that there is a relationship between the utility and the price the consumer is willing to pay,p(x) = v’(x)For this case, although not in general, this price does not depend on the consumer income m.The inverse demand function p(x) has the following interpretation:The incremental price the consumer is willing to pay for one more unit of widgets, after already buying x units, is p(x).If we were to plot quantity of widgets on the vertical access and price on the horizontal axis, it would be called a demand function.By integrating both sides of the equation above, we can determine the utility function from the inverse demand function,v(x) - v(0) = integral of p(s) from s=0 to s=xAgain, this simple relationship holds because of the quasilinear utility assumption, with the simplification that the consumer income is irrelevant. Note again that the utility function is not unique, so this is only one feasible utility consistent with the demand curve.Copyright 1997, David G. Messerschmitt 3/5/97 5Inverse demand functionInverse demand functionp(x)Quantity ofwidgets xThe inverse demand function p(x) measures theprice the consumer is willing to pay foreach additional unit of widgetsThe consumer won’t buy any more widgets than thisThe consumer is willing to pay a lot for the first widgetCopyright 1997, David G. Messerschmitt. All rights reserved.The assumption of a fixed price is a common case. Alternative pricing strategies would be to sell different versions at different prices (covered later), or provide a quantity discount (charge more per unit widget as the total widgets purchased gets larger).Copyright 1997, David G. Messerschmitt 3/5/97 6Quantity consumed vs. price Quantity consumed vs. price chargedchargedp(x)Quantity ofwidgets xAssume the producer of


View Full Document

Berkeley COMPSCI 294 - Economics tutorial

Documents in this Course
"Woo" MAC

"Woo" MAC

11 pages

Pangaea

Pangaea

14 pages

Load more
Download Economics tutorial
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view Economics tutorial and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view Economics tutorial 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?