Question

2 .Suppose the production function of a firm is given by f (x1, x2) = 2x1 + 4x2

(a) Calculate the conditional demand functions of the firm assuming w1 = 2; w2 = 3, and y = 8

(b) Calculate the minimum cost of the firm to produce 8 units of the good when w1 = 2 and w2 = 3

Answer #1

y = f(x1, x2) = 2x1 + 4x2

Total cost = w1.x1 + w2.x2 = 2x1 + 3x2

(a) A linear production function means x1 and x2 are substitutes and isoquant is linear, touching both axes. Optimal solution lies on one of the corner points, signifying that either x1 or x2 are consumed.

y = 8 = 2x1 + 4x2

When x1 = 0, x2 = 8/4 = 2 and Total cost = 2 x 0 + 3 x 2 = 6

When x2 = 0, x1 = 8/2 = 4 and Total cost = 4 x 2 + 0 x 3 = 8

Since total cost is lower when x1= 0 and x2 = 2, this is the optimal bundle.

With given data,

**Conditional demand for x1 = 0**

**Conditional demand for x2 = 2**

(b) With given values and x1 = 0 & x2 = 2, total cost for 8 units is

**Cost =** 2 x 0 + 3 x 2 = 0 + 6 =
**6**

Suppose the production function of a firm is given by f (x1; x2)
= min{x1, x2}
(a) Calculate the conditional demand functions of the firm
assuming w1 = 2; w2 = 4, and y = 8
(b) Calculate the minimum cost of the firm to produce 8 units of
the good when w1 = 2 and w2 = 4:

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(a) Find the levels of the inputs that maximize the profits of
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A firm’s production function is given as y=(x1)^(1/2) *
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as w1>0 and w2>0,
respectively. Answer the following questions.
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Derive the long-run conditional input demand functions and the
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the following production function: f(x1, x2) = min {x1, x2} +
x2
Input 1 costs w1 > 0 per unit and input 2 costs w2 > 0 per
unit.
(a) Draw the isoquant associated with an output of 4. Make sure
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x11/2x21/3. The price
of factor 1 is w1 = 12
and the price of factor 2 is w2 = 1.
With x̄2 = 8, find the short-run cost function c(y).
Find short-run AC(y), AVC(y), and MC(y) based on the answer to
a.
Write out the long-run cost minimization problem to find the
cheapest way to produce y units of output.
Write out the Lagrangian for the long-run cost minimization
problem.
Solve the long-run...

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x2)1/2, where x1 is the amount of plastic and x2 is the amount of
wood used. If the cost of plastic is $4 per unit and the cost of
wood is $4 per unit, then what is the cost of producing 8 deer
?

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Consider a firm whose production technology can be represented
by a production function of the form q = f(x1, x2) = x α 1 x 1−α 2
. Suppose that this firm is a price taker in both input markets,
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input two being w2 per unit. 1. Does this production technology
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In Problem 12, Al’s production function for deer is
f(x1, x2) =
(2x1 + x2)1/2,
where x1 is the amount of plastic and
x2 is the amount of wood used. If the cost of
plastic is $8 per unit and the cost of wood is $1 per unit, then
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a.
$49.
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$28.
c.
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d.
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e.
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step by step, please

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