$1.(6$ points$).$ This problem is based on the specific factors model. Consider the economy of the Shire that

produces cereals and swords. Each industry employs Hobbits, but land is specific to the production of

cereals, and metal is a specific factor in the sword industry. The amounts of land $($L$)$ and metal $($M$)$ are

L$=1000$ and M$=40,$ and there are $100$ Hobbits in Shire. The production functions and the marginal products

of Hobbits' labor are as follows:

C $=8($HC $)0\mathrm{.}5($L$)0\mathrm{.}5,$ MPHC $=4($L$)0\mathrm{.}5/($HC $)0\mathrm{.}5$

S $=4($HS $)0\mathrm{.}5($M$)0\mathrm{.}5,$ MPHS $=2($M$)0\mathrm{.}5/($HS $)0\mathrm{.}5$

where C is the cereal output in pounds, S is the number of swords produced, and HC and HS are the numbers of

Hobbits employed in the cereal and sword sectors$,$ respectively.

$($a$)$ Assume that the price of $1$ pound of cereals is $$10$ and the price of a sword is $$200.$ Draw the equilibrium

diagram $($the figure that is similar to Figure $3-4)$ for this economy.

$($b$)$ What is the wage rate paid to Hobbits in the Shire? How many Hobbits work in each sector?

$($c$)$ Because of the War of the Ring, the price of a sword went up to $$300.$ Calculate new wage and employment

level in each sector.

$($d$)$ Do Hobbits gain or lose if the price of a sword goes up to $$300?($To answer the question, calculate their

real wages before and after the price change$).$

$2.(4$ points$).2$ countries, Gryffindor and Slytherin, produce $2$ goods, magic potions $($denoted by MP$)$ and

magic wands $($denoted by MW$).$ Assume that lemon grass $($denoted by G$)$ is a factor specific to magic potions,

magic oak $($denoted by O$)$ is a factor specific to magic wands, and troll labor $($denoted by L$)$ is free to move

between $2$ sectors$.$

$($a$)$ Consider Gryffindor. Holding constant the price of magic potions, suppose the decrease in the price of

magic wands is $10\%$ and the decrease in the troll wage is $4\%.$ Determine the impact of these changes on the real

rentals on lemon grass and magic oak by using information below:

Magic potions:

Sales revenue PMPQMP $=75$

Payments to troll labor WLMP $=50$

Payments to lemon grass owners RG G $=25$

Magic Wands:

Sales revenue PMW QMW $=600$

Payments to labor WLMW $=200$

Payments to magic oak owners RO O $=400$

$($b$)$ How would your answer in part $($a$)$ change if the $4\%$ decrease in the troll wage was caused by the decrease