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(a) A representative consumer has a utility function U (x, y) = xy. A representative firm makes good x and has a product...

(a) A representative consumer has a utility function U (x, y) = xy. A representative firm makes

good x and has a production function x = f(k, l) = (kl)0.25and an unavoidable fixed cost

equal to A. There are 100 consumers and, initially, 100 firms. Prices are w = v = Py = 1 and Px is determined in a competitive market. Representative consumer income is I = 2.

(a) Find the representative individual’s Marshallian demand for good x?

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Answer #1

Marshallian demand function, where

MUx/MUy =Px/Py

MUx/MUy = y/x

Px/Py =Px/1

y/x = Px/1

Y = Px*X

Put the value of Y in budget constraint to find Marshallian demand of X

I = Px*X + Py*Y

I = 2 [ given]

2 = Px*X + Py*[Px*X]

Put Py = 1,

2 = Px*X + Px*X

2 = 2Px*X

X = 2/ 2*Px

X = 1/Px--- Marshallian demand for good X

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