$1.$ The demand function is Q $=100-8$p$,$ and the supply function is Q $=30+6$p$.$ Determine the equilibrium price and quantity.

$2$a$.$ Calculate to three decimal places the price and cross$-$price elasticities of demand for coconut oil. The coconut oil demand function is

Q $=1200-12$p $+16\mathrm{.}2$pp $+0\mathrm{.}25$Y $,$

where Q is the quantity of coconut oil demanded in thousands of metric tons per year, p is the price of coconut oil in cents per pound, pp is the price of palm oil in cents per pound, and Y is the income of consumers. You will need to calculate the income of consumers first. Assume that p is initially $45$ per pound, pp is $31$ per pound, and Q is $1375$ thousand metric tons per year. The coefficients for p and pp are consistent with prices expressed in $$ per pound, not $ per pound.

$2$b$.$ Using the coconut oil demand function from question $2$a$,$ calculate to four decimal places the income elasticity of demand for coconut oil.

$3.$ Ghose and Han $(2014)$ found that the elasticity of demand for Google Play apps is $-3\mathrm{.}7.($See the mini$-$case: Demand Elasticities for Google Play and Apps.$)$ This elasticity applies to a small college town where approximately $1,000$ apps per month are sold.

$3$a$.$ If the price rises by $10\%,$ what would be the effect on quantity demanded?

$3$b$.$ What is the percentage change in revenue? $($revenue $=$ price x quantity$)$ Be sure to include a negative sign, if needed.

$4.$ Using the data in Table $3\mathrm{.}1$ of the text $($pp$.58$ of the print version$),$ estimate the $($inverse$)$ cod demand function. You can do the estimate in Excel using the "add trendline" option in a plot or using Excel's regression package. If you do not have Excel, any regression package will do$.$ Remember to use the inverse demand funaciton.

$5.$ In the Camry focus group analysis in Chapter $3($pp$.65-67$ in the print version$),$ a regression is used to estimate the demand for Toyota Camrys. Using the estimated equation Q $=53\mathrm{.}857-1\mathrm{.}438$p$,$ where p is is thousands of dollars and Q is in thousands of vehicles:

a$.$ How many fewer Camrys would we expect the focus group to purchase if the price were increased by $$1000?$

b$.$ How many Camrys would we expect the focus group to purchase if the price is $$22,000?$

c$.$ What is the price elasticity of demand if the price is $$22,000?$

$6.$ You work for a firm producing fitness equipment. You have been told that the demand for the firm's main product $--$ a multi$-$station home gym $--$ is inversely related to its price $($p$).$ You have surmised correctly that the demand function is Q $=$ a $+$ b$/$p $,$ where a and b are parameters to be estimated. You have been provided with price and quantity data obtained from focus groups and have been asked to run a regression of revenue $($p$*$Q$)$ on price. Should you use a functional form where revenue is also inversely related to price $--$ or something else? Explain.