Question $3(25$ points$)$

A firm sells its product in two countries: Japan and Canada.

The marginal cost is $$20,$ and total fixed cost is $$50.$

The direct market demand functions in the two countries are as follows:

QJ $=1202$PJ and QC $=400\mathrm{.}5$PC$,$

where the subscript J denotes Japan, and the subscript C denotes Canada.

$3\mathrm{.}1(3$ points$)$ Derive the firm$$s total cost function, TC $=$ f$($Q$),$

where Q $=$ QJ $+$ QC$.$

$$ TC $=$

$\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

$3\mathrm{.}2(12$ points$)$ Suppose the firm can prevent resale from one market to the

other $($i$.$e$.,$ a product sold in Japan will not be resold in Canada, and vice versa$).$

a$)(4$ points$)$ What quantity and price does the firm sell in Japan to

maximize profit?

$$ QJ$*=\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$ units.

$$ PJ$*=$ $ $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

b$)(4$ points$)$ What quantity and price does the firm sell in Canada to

maximize profit?

$$ QC$*=\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$ units.

$$ PC$*=$ $ $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_9$

c$)(4$ points$)$ Given the information in Question $3\mathrm{.}2,$ if the firm were able to

set different prices for sales in Japan and Canada, what would be the

firm's total profit $($DP$)?$

$$ DP $=$ $ $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

$3\mathrm{.}3(10$ points$)$ Suppose the firm cannot prevent resale of its products,

which means it will have to use a single$-$pricing strategy for both Japan

and Canada. This, in turn, implies that the price of a product sold in Japan

and Canada will be identical.

a$)(4$ points$)$ Derive the direct total market demand function, Q $=$ f$($P$),$

where PJ$=$ PC $=$ P$.$

$$ Q $=$

$\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

b$)(6$ points$)$ Given the information in Question $3\mathrm{.}3,$ what would be the

profit$-$maximizing quantity $($Q$*),$ price $($P$*),$ and total profit $($SP$)?$

$$ Q$*=$

$\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

units.

$$ P$*=$ $ $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

$$ SP $=$ $ $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$