Thursday
April 2, 2015

Homework Help: ECONOMICS - Perfect Competition

Posted by Anonymous on Monday, November 2, 2009 at 7:41am.

Please check and correct my answers. Thank you.

1) Jack Benny can get blood from a stone. If he has x stones, the number of pints of blood he can extract from them is f(x) = 2x^(1/3). Stones cost Jack w dollars each. Jack can sell each pint of blood for p dollars.

a) How many stones does Jack need to extract y pints of blood?

b) What is the cost of extracting y pints of blood?

c) What is Jack’s supply function when stones cost w each? When stones cost $8 each?

d) If Jack has 19 relatives who can also get blood from a stone in the same way, what is the aggregate supply function for blood, Y, when stones cost w dollars each?

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my answers:

1)

a)
y^3/8

b)
(w)(y^3/8)

c)
S(p,w) = (8p/3w)^(1/2)
S(p) = (p/3)^(1/2)

d)
Y = 20(8p/3w)^(1/2)




2) Earl’s production function is f(x1, x2) = x1^(1/2) * x2^(1/3), where x1 is the number of pounds of lemons he uses and x2 is the number of hours he spends squeezing them. His cost function is c(w1, w2, y) = 2w1^(1/2) * w2^(1/2) * y^(3/2), where w1 is the cost per pound, w2 is the wage rate, and y is the number of units of lemonade produced.

a) If lemons cost $1 per pound, the wage rate is $1 per hour, and the price of lemonade is p, find Earl’s marginal cost function and his supply function. If lemons cost $4 per pound and the wage rate is $9 per hour, what will be his supply function be?

b) In general, Earl’s marginal cost depends on the price of lemons and the wage rate. At prices w1 for lemons and w2 for labour, what is his marginal cost when he is producing y units of lemonade? The amount that Earl will supply depends on the three variables, p, w1, w2. As a function of these three variables, what is Earl’s supply?


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my answers:

2)

a)
MC(y) = 3y^(1/2)
S(p) = p^2/3
S(p) = p^2/18

b)
MC(w1, w2, y) = 3w1^(1/2) * w2^(1/2) * y^(1/2)
S (p, w1, w2) = p^2 / (3 w1 * w2)

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