Answer to Question #191469 in Economics of Enterprise for Faisal

Question

The table below shows the quantities of coffee produced by the 4 major producers in 2005.

We’ll suppose that these are the only producers. These quantities are expressed in bags. (A

bag of coffee has a weight of approximately 132 pounds). Additionally, we know that the

price of coffee in 2005 was approximately 172 USD per bag (172000 USD per thousand bags).

Producer Bags exported (in thousands)

Brazil 26198

Vietnam 13432

Colombia 10871

Indonesia 6744

Suppose that a Cournot model with a linear demand and constant marginal costs is a good

representation of this market. The demand is 𝑃 = 𝑎 − 𝑄.

b) Suppose that in 2006 the marginal cost of Brazil increases by 10% due to a drought. (This

actually happens from time to time).

i) What would be the effect on the international price of coffee?

ii) On the consumer surplus?

iii) On the market shares of each producer?

r?

Answer 1

$$Solution$$

$Q= q1+q2+q3+q4= 26198+13432+10871+6744 = 57245 (In\ thousands)$

since it is given that $P= \$172000 (For \ Q=1 \ or\ for \ 1\ thousand \ bags)$

We get:

$172,000 = a - 57245$

$a=229,245$

b) For marginal costs of each producer, the 4 equations are given:

$q1=\frac {a-4c1+c2+c3+c4}{5}$

and similarly for $q2, q3 \ and\ q4\ i.e.$

$q2= \frac{a +c1 -4c2+c3+c4}{5}$

$q3= \frac{a+c1+c2-4c3+c4}{5}$

$q4=\frac {a+c1+c2+c3-4c4}{5}$

inserting values of$\ q1,q2,q3,q4$ and$\ a$ , we have $4$ equations in $4$ variables $c1, c2, c3\ and \ c4$

$(26198\times5)-a = -4c1+c2+c3+c4$

$-98,255 = -4c1+c2+c3+c4$

and similarly:

$(13432\times5)-a = c1-4c2+c3+c4$

$-162,085 = c1-4c2+c3+c4$

$(10871\times5)-a=c1+c2-4c3+c4$

$-174,890= c1+c2-4c3+c4$

$(6744\times5)-a=c1+c2+c3-4c4$

$-195,525=c1+c2+c3-4c4$

solving these $4$ equations in$\ 4$ unknowns, we get

$c1= 145,802$

$c2= 158,568$

$c3= 161,129$

$c4= 165,256$

Therefore these are the marginal costs of each producer

$145,802$ for Brazil

$158,568$ for Vietnam

$161,129$ for Colombia

$165,256$ for Indonesia.

[B]

i ]The prices will increase-marginal cost increases as quantity goes up therefore there will be need to transfer the costs/ cover the costs hence the prices will increase.

ii]There will be reduced consumer surplus.

iii]Brazil- there will be reduced market shares as price increases due its being affected by increase of marginal costs.

Vietnam , Colombia and Indonesia- there will be increased market share.