<p>(a) Price elasticity is $\eta_d=\frac{\partial Q}{\partial P} \cdot \frac{P}{Q}$. Therefore you get $\eta_d=-2 \cdot \frac{2}{10-2\cdot2}= -\frac{2}{3}$.</p>

<p>(b) $Q=10-2 \cdot 3 = 4$. Total expenditure is $3 \cdot 4 = 12$. At a price of 5 units, there is no demand. The consumer surplus for linear demand functions follows $\frac{1}{2}\left(p_{max}-p\right)\cdot x$ with $p_{max}$ as the price where there is no demand. Consumer surplus therefore is $\frac{1}{2}\left(5-3\right)\cdot 4=4$.</p>

<p>(c) Total expenditure $TR$ follows $TR=p \cdot x$. For maximizing $TR$ just derive it (and set it to zero) and you get $\frac{\partial TR}{\partial p}=\frac{\partial 10p-2p^2}{\partial p}=10-4\cdot p = 0$. This gives the value $2.5$ for $p$. On how to calculate elasticity see (a).</p>

<p>(d) Total expenditure for $p=1$ is $8 \cdot 1 = 8$, for $p=2$ it is $6 \cdot 2 = 12$. If price increases from 1 to 2, $TR$ increases. Look the result in (c), that $p=2.5$ maximizes $TR$. Therefore from $p=1$ to $p=2$, $TR$ has to increase. In equivalent, $TR$ has to decrease when price rises from $p=3$ to $p=4$.</p>

CC BY-SA 3.0
2017-09-14T15:08:15.257Z
[Should I](https://economics.meta.stackexchange.com/questions/1662/should-i-downvote-valid-answers-to-off-topic-questions)?
Giskard
CC BY-SA 3.0
2017-09-14T18:11:55.940Z
@denesp what is clear is that der_bosmann [should have not](https://meta.stackexchange.com/questions/133552/should-i-answer-off-topic-questions).
luchonacho
CC BY-SA 3.0
2017-09-15T09:22:11.743Z
Thanks for your helpful comments. As i am pretty new to the SE community, i try my best to contribute to this platform. I will keep your comments in mind for the future, but [please](https://meta.stackexchange.com/q/9953).
skoestlmeier
CC BY-SA 3.0
2017-09-14T13:39:27.123Z
2017-09-14T13:39:27.123Z
skoestlmeier
<blockquote>
<p>Oscar’s demand for movies is given by Q = 10−2P.</p>
<p>(a) What is the price elasticity of demand at a price of 2? Is Oscar’s demand elastic or inelastic at a price of 2?</p>
<p>(b) Assume that the price is 3. What is Oscar’s total expenditure on movies? What is the consumer surplus?</p>
<p>(c) What is the price that maximizes Oscar’s total expenditure on movies? What is the price elasticity of demand at this price?</p>
<p>(d) If the price increases from 1 to 2, does Oscar’s total expenditure on movies rise or fall? If the price rises from 3 to 4, does Oscar’s total expenditure on movies rise or fall?</p>
</blockquote>

CC BY-SA 3.0
2017-09-14T14:25:48.203Z
https://www.chegg.com/homework-help/questions-and-answers/oscar-s-demand-movies-given-q-10-2p-price-elasticity-demand-price-2-oscar-s-demand-elastic-q14733309
london
CC BY-SA 3.0
2017-09-14T16:34:46.597Z
Hi, Welcome to Economics SE! we have a policy regarding homework questions where we require that you show some work before an answer is provided. More on this topic here: https://economics.meta.stackexchange.com/questions/1465/economics-se-policy-on-homework-questions
EconJohn
<microeconomics>
Microeconomics for demand
Bart Scott
# Microeconomics for demand

(Asked by: username_0 on 2017-09-14)

> Oscar’s demand for movies is given by Q = 10−2P.
>
> (a) What is the price elasticity of demand at a price of 2? Is Oscar’s demand elastic or inelastic at a price of 2?
>
> (b) Assume that the price is 3. What is Oscar’s total expenditure on movies? What is the consumer surplus?
>
> (c) What is the price that maximizes Oscar’s total expenditure on movies? What is the price elasticity of demand at this price?
>
> (d) If the price increases from 1 to 2, does Oscar’s total expenditure on movies rise or fall? If the price rises from 3 to 4, does Oscar’s total expenditure on movies rise or fall?

**Tags:** microeconomics
> **Comments:**
> **username_1**: https://www.chegg.com/homework-help/questions-and-answers/oscar-s-demand-movies-given-q-10-2p-price-elasticity-demand-price-2-oscar-s-demand-elastic-q14733309  
> **username_2**: Hi, Welcome to Economics SE! we have a policy regarding homework questions where we require that you show some work before an answer is provided. More on this topic here: https://economics.meta.stackexchange.com/questions/1465/economics-se-policy-on-homework-questions  

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## 1 answers

### Answer by username_3 on 2017-09-14. Score: -1 | Accepted answer

(a) Price elasticity is $\eta\_d=\frac{\partial Q}{\partial P} \cdot \frac{P}{Q}$. Therefore you get $\eta\_d=-2 \cdot \frac{2}{10-2\cdot2}= -\frac{2}{3}$.

(b) $Q=10-2 \cdot 3 = 4$. Total expenditure is $3 \cdot 4 = 12$. At a price of 5 units, there is no demand. The consumer surplus for linear demand functions follows $\frac{1}{2}\left(p\_{max}-p\right)\cdot x$ with $p\_{max}$ as the price where there is no demand. Consumer surplus therefore is $\frac{1}{2}\left(5-3\right)\cdot 4=4$.

(c) Total expenditure $TR$ follows $TR=p \cdot x$. For maximizing $TR$ just derive it (and set it to zero) and you get $\frac{\partial TR}{\partial p}=\frac{\partial 10p-2p^2}{\partial p}=10-4\cdot p = 0$. This gives the value $2.5$ for $p$. On how to calculate elasticity see (a).

(d) Total expenditure for $p=1$ is $8 \cdot 1 = 8$, for $p=2$ it is $6 \cdot 2 = 12$. If price increases from 1 to 2, $TR$ increases. Look the result in (c), that $p=2.5$ maximizes $TR$. Therefore from $p=1$ to $p=2$, $TR$ has to increase. In equivalent, $TR$ has to decrease when price rises from $p=3$ to $p=4$.

> **Comments:**
> **username_4**: [Should I](https://economics.meta.stackexchange.com/questions/1662/should-i-downvote-valid-answers-to-off-topic-questions)?  
> **username_5**: @denesp what is clear is that der_bosmann [should have not](https://meta.stackexchange.com/questions/133552/should-i-answer-off-topic-questions).  
> **username_3**: Thanks for your helpful comments. As i am pretty new to the SE community, i try my best to contribute to this platform. I will keep your comments in mind for the future, but [please](https://meta.stackexchange.com/q/9953).  

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