Question $2($Third degree price discrimination$)$

Feed$-$forward Drug Corporation sells a major drug in Europe and in the United States. Because of legal

restrictions, the drug cannot be bought in one country and sold in another. The demand curve for the

drug in Europe is

$P_E=16-Q_E,$ where $P_E$ is price in $ per pound in Europe and $Q_E$ is the amount in millions of pounds

sold there.

The demand curve for the drug in US is

$P_U=34-2Q_U,$ where $P_U$ is price in $ per pound in the US and $Q_U$ is the amount in millions of pounds

sold there.

The total cost in millions of dollars of producing the drug for sale worldwide is

$TC=8+2(Q_E+Q_U)$

a$)$ Derive the firm's total profit function including both Europe and the US in it as a function of $Q_E$ and

marks$]$

b$)$ Calculate the optimal number of drugs to sell in Europe as well as in the US$.[6$ marks$]$

c$)$ Calculate the optimal prices to charge in Europe as well as in the US$.[4$ marks$]$

d$)$ Calculate the firm's total profit under this price discrimination scheme. $[3$ marks$]$

a$)$ To derive the total profit function, I need to calculate the relenue and cost cumcton fists,

Revenue in $E_U$ opl: $R_E=P_E{Q}_E{R}_E=(16-Q_E)Q_E{R}_E=16Q_E-Q_E^2$

Revenue in US: $RU=P{P}_U{Q}_U{R}_U=(34-2Q_U)Q_U{R}_U=34Q_U-2Q_U^2$

otal Revence $=R_E+R_u=16Q_E-Q_E^2+34Q_u-2Q_u^2$

otal cost $=8+2(Q_E+Q_0)$ Last for the tond profit fandion $=R-Tc$

$=(16Q_E-Q_E^2+34Q_v-2Q_v^2)-(8+2(Q_E+Q_0))$

$=-Q_E^2+14Q_E-2Q_u^2+32Q_u-8$

So to find the opt:mal number of draug b soll, must maximize in bral profit faurto with respat

QE and QU$.$ Find the partial derintives ond sot to equal Zero. d$)$ Firmis total profit under this priee

To oftrol

Now for the optimal prices to Charge in Eupe and US$.$ Sub in the optimal quasies

urope: $P_E=16-Q_E{P}_E=16-7P_E=9$ eurosperfowl

$Q_E$ and $Q_U$ inds demed finction

S: $P_v=34-2Q{P}_v=34-2(8)P_U=34-16P_v=18$ doler

Thats the context for the for Question A on Question $3$

$a$

b$)$ Now for the Profit Aunction

$()=P*Q-TC$

$=(18-0\mathrm{.}67Q)*Q-(6+2Q)$

$=18Q-0\mathrm{.}67Q^2-6-2Q$

$=16Q-0\mathrm{.}67Q^2-6$

c$)$ To find the optimal price and quality in case of no price discriomustion.

Must differentide the profit function with resect to $Q$

$\frac{d}{dQ}=16-1\mathrm{.}340=0,P=18-0\mathrm{.}670$

$1\mathrm{.}34Q=16,=18-0\mathrm{.}67(12)$

$Q=11\mathrm{.}94,=18\mathrm{.}8\mathrm{.}04$

$=9\mathrm{.}96$

$12$

$=192-96\mathrm{.}48-6$

d$)$ The firmis optiral procits, Just sno and salve

This is what i have but i think its wrong, could you please help