Question

1) Adam has found that the number of plants, H, depends on the amount of light, L, and
water, W. Adam’s production function is H= min{L,2W)
a) Suppose Adam is using 1 unit of light, what is the least amount of water he can use
and still produce 1 plant?
b) If suppose Joe wants to produce 4 plants, what are the minimum amounts of light
and water required?
c) Find Adam’s conditional factor demand for light and water.
d) Assume that each unit of light costs w1 and each unit of water costs w2. Find Adam’s
cost function.

Answer 1

H= min{L,2W)

Now, L = 1

To produce 1 plant ie H = 1, W must be = 0.5

H = Min(1,2*.5)

H = Min(1,1)

H = 1

So, 1/2 unit of water to used to produce 1 plant

b)

Production takes place along a ray of origin where,

At equilibrium, L = 2W = 4

So, L* = 4

and W* = 2

Minimum amount of light and water required(L,W) = (4, 2)

c)

Conditional Factor Demands: L* = H

2W* = H

W* = H/2

d)

Cost Function: C* = w1*L +w2*W

C* = w1*H + w2*(H/2)

C* = H*(w1 + w2/2)

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