This problem is based on the specific factors model. Consider the economy of the

Question

This problem is based on the specific factors model.

Consider the economy of the Kingdom of the North that produces creals and snowmen. Each industry employs White Walkers, but land is specific to the production of cereals, and magic is a specific factor in the snowmen industry. The amounts of land (L) and magic (M) are L=1 and M=16, while the population size of the Kingdom in the North is 10 White Walkers. The production functions and the margincal products of White Walker's labor are as follows:

C=(Wc)^0.5(L)^0.5,   MPWc=0.5(L)^0.5/(Wc)^0.5

S=(Ws)^0.5(M)^0.5,  MPWs=0.5(M)^0.5/(Ws)^0.5

where C is the cereal output in pounds, S is the number of snowmen produced, and Wc and Ws are the numbers of White Walkers employed in the cereal and snowmen sectors, respectively.

(a) If the price of 1 pound of cereals is $2 and the rice of a snowman is $8, what is the wage rate paid to White Walkers in the Kingdom of the North? How many White Walkers work in the cereal sector? In the snowmen sector?

(b) Since "Winter is Coming", the price of a snowman went down to $4. Calculate the new wage and emplooyment level in each sector.

(c) Do the White Walkers gain or lose if the price of a snowman goes down to $4? (To answer the question, calculate their real wages before and after the price change).

Explanation / Answer

a) If the price of 1 pound of cereals is $2 and the rice of a snowman is $8,

wage rate paid to White Walkers in the Kingdom of the North =

For cerals ,As in equilibrium ,MPW = W/P

=> MPWc= Wc/2

=>0.5(L)^0.5/(Wc)^0.5 =Wc/2 as given L=1

=> 0.5*(1)^0.5 *2 = Wc^1.5

=> Wc = 1^1/3 = $1

so wage for working in cerals sector =$1 , similarly forsnowmen sector

=>MPWs =Ws/P

=> 0.5(M)^0.5/(Ws)^0.5 = Ws/8

=> 0.5(16)^0.5/(Ws)^0.5 = Ws/8

=> Ws = 6.349 =$6.35

so wage in snowden sector(Ws) =$6.35

and White Walkers work in the cereal sector=4 and White Walkers work in the snowmensector = 6

b)

Winter is Coming", if the price of a snowmen went down to $4 then

only snowmen sector wage change => MPWs =Ws/P

=> 0.5(16)^0.5/(Ws)^0.5 = Ws/4

=>Ws =$4

so wage in snowmen sector =4 and employment = 6 as there is no price change for cerals.

c) real wage initially = 6.35/8 =$0.79

and real wage in winter =4/4 =$1. So as they have to pay more now than initial. so White Walkers lose if the price of a snowman goes down to $4

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