The Sons of Knute had a hunting lodge up on Loon Lake which burned down last winter. They plan to rebuild it this summer and are trying to decide how large the new lodge should be. The organization has 50 members. The marginal rate of substitution of each of them between square feet of hunting lodge and money for other goods is 1.2-.0004y where y is the size of the hunting lodge in square feet. What is the ecient size for the new hunting lodge?

y = 2,250 sq.ft  

Hence, 2,250 sq.ft is the efficient size for the new hunting lodge.

Note: It can vary according to the cost per sq.ft. In this problem, we have assumed it as $15.

Explanation:

Data Given:

Organization members = 50

Equation given = 1.2 - 0.0004y = for the goods and size of the lodge.

where, y is the size of the hunting lodge in sq.ft.

Required = What is the efficient size for the new hunting lodge? = So, we need to find the value of y.

Solution:

First of all, we need to assume the cost for each sq.ft required to build this hunting lodge. As we have not given the cost. If we do not put the value then we will get a general answer in terms of variables. So, it is better to assume some value.

Let's assume the value = $15 per sq.ft

And we have 50 members in the organization so, multiply it with the equation given above.

X = 50 x (1.2 - 0.0004y)

X = 60 - 0.02y

So in order to find y, we need to equate this X to our assumed value of $15.

60 - 0.02y = 15

60 - 15 = 0.02y

45 = 0.02y

y = 2,250 sq.ft  

Hence, 2,250 sq.ft is the efficient size for the new hunting lodge.

Note: It can vary according to the cost per sq.ft. In this problem, we have assumed it as $15.