ECON201PSet1Answers - W ELLESLEY COLLEGE D EP ARTMENT O F E...

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WELLESLEY COLLEGE DEP ARTMENT OF ECONOMICS ECONOMICS 201-03 JOHNSON Answers to Problem Set #1 1. The activities of TV, Radio, AND Internet Advertising DO exhibit diminishing returns, because each extra (marginal) $1 OOK spent on each of them adds LESS and LESS to beer sales .... more is less better. Now, however, if we allow for the possibility of Internet advertising with the numbers given, it is no longer optimal to spend $800K on TV and $200K on radio. Ifwe look at MARGINAL benefits, then the first $1 OOK should be spent on Internet advertising, because its marginal benefit (5000 barrels) is greater than either TV (4750) or Radio (950). The next $800K, however, should be spent on TV advertising, as the marginal benefit of each of the $lOOK's on TV up to $800K exceed 1000 barrels (the marginal benefit of the second $100K spent on Internet advertising). What about the final $100K, now that you've spent $100K on the Internet and $800K on TV? With ~that final $ lOOK, you could either get 750 barrels with TV, 950 with radio, or 1000 with the Internet. Go for the Internet. Thus, in this problem, it is never profitable to use radio advertising. Spend $800K on TV and $200K on the Internet fora total of30,000 barrels sold. Note also that you should spend the $1 OOK amounts in the right order: the first $lOOK on the Internet, followed by $800K on TV, and THEN the final $1 OOK back on the Internet. What if you start by spending $200K on the Internet, with the idea of spending the REST of your money ($800K) on TV. BUT, the advertising manager calls to tell you the budget has been cut in half, let's say. Then, you won't have maximized sales of the remaining $500K because you different spend in the right order. .... 2. a. Using the point elasticity form, we would have: \5" - LO (ic~~ ~ CD ::; 20 -2sCJ~ -\ Itt - - - - _ . -3 - ~f~b.~ ~ ~-3 - -t- . -3'"3~1 3 - -1 \ I) If ~ ~~.~ ~,,,,, ~ \<; .-3/4- C)\' ~~~~~~ ,,~ It " f·1SJ m
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b. With our calculated elasticity, we need to fit the given data into a demand function of the form: QD = a - b*P Given that the demand curve is linear, we KNOW that the elasticity is NOT. Thus, our elasticity calculation from (a) can be integrated into our general expression for elasticity as follows: _ C~ ~ _ c-_·-- D Q Now, plug in either point (I'm using the "Before" point, but it's also acceptable to use the "After" point) to now solve for b 20 ~ l~J ~) 3 Now, we can return to the demand function above and use our calculated b value with either point on the demand curve to solve for the value of a : b - Q ~ V\. - 5 r ~) ~S\~~ \~\~~ l l 0 ~ c, - s ls) -;::: ) ~ ~ '3 S [0." -:. 35 - Sf' \ c. A demand function of the constant elasticity form would resemble: As we know, this demand function has a constant elasticity of -b , s~o already we know that our answer will take the form: ~ D ;; 0 ..... ? l-' ~ Jtf-) All that remains is to find the value of a ,which we can do by using one of our data points: ( (\~~ \ '(\, Q \l;'V S Ii-<:,{ ~t" 'bJ; Q. I) 0')' ~() ~ <k "3 ~ 31 t --'} ,,~ CdO'> (?::>~)~ =[ Its ~ - 3/'f :: LtS.6,· s j [Author's Note: Your answers mIght differ slightly from those here if you decided to use the other data point when solving for a and/or b, and that's just fine.]
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a.
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