$(24$ points$)$ Suppose Mr$.$ Beast is touring$/$putting on a show at various venues across

North America. Furthermore assume one of the shows will take place in Vancouver

in May $2024.$ The hypothetical event will be held at BC Place in front of a sold out

crowd $($ ~~$54,000$ seats$).$ Suppose there are two types of Mr$.$ Beast fans: fanatical Mr$.$

Beast fans and the average Mr$.$ Beast fans.

As the event is attracting a large crowd, a large number of food vendors will be just

outside $BC$ place selling quick meals. The crowds will have a market demand for meals

that will depend on the type of fan. Suppose the demand for each Fanatical Mr$.$ Beast

fan is:

$q_F^D=1-\frac{1}{28}P$

The demand for each Average Mr$.$ Beast fan is:

$q_A^D=1-\frac{1}{20}P$

As the number of food vendors is large we will model this as a perfectly competitive

market with quick meals being identical. This means we can use the market supply

curve. Suppose the supply curve is:

$Q^S=-18,750+3,750P$

Use the information above to answer the questions below:

$($a$)(3$ marks$)$ Find the aggregate demand curve for quick meals given there are $14,000$

Fanatical Mr$.$ Beast fans and $40,000$ Average Mr$.$ Beast fans attending the tour.

$($b$)(4$ marks$)$ What is the equilibrium outcome of the market? What is the producer

surplus and what is the consumer surplus?

$($c$)(3$ marks$)$ If you calculate the consumer surplus for each group independently,

you should find the overall consumer surplus for Fentieel and the Average Mr$.$

Beast fans are identient is $$2,977\mathrm{.}20$ more than Fanatical fans $($it may be helpful

to calculate the per person consumer surplus instead$).$ Explain $($in words$)$ what

we learn from this information about consumer surplus. Is it consistent with the

description of the fan types? $($Note: should be a $2-3$ sentence answer, do not

make it overly complicated.$)$

$($d$)(5$ marks$)$ Create a graph of the supply and demand with the equilibrium and

surpluses labelled. Be sure to properly label all parts of the graph including both

the $x$ and $y$ axis.

$($e$)(3$ marks$)$ Suppose the government imposes a tax driving the price of a quick meal

up to $$12\mathrm{.}90$ and the tax incidence on consumers is $60\%.$ What is the value of the

per unit tax? What's the government revenue? How large of a deadweight loss

would exist?