Question 1

The Lost Mountains of northern Iowa are inhabited by the rare Marshallian deer.Patches of grass are far apart in this rugged land.If a deer finds a fresh patch of grass and spends h hours grazing it, it gets the square root of h units of grass.The deer compete for grass.When there are n deer, it takes a deer n 2 minutes to find a fresh patch.A deer can survive if it gets 1 unit of grass every 200 minutes.
a.Find the average cost in time of a unit of grass if a deer gets y units of grass from each patch.
b.How much time will an efficient deer spend in each patch when there are n deer? (Hint: Minimize aver-age cost.)
c.Since there is free entry into the deer business, the equilibrium population is the maximum number of efficient deer who can survive.How many is this?

Accepted Answer

The answer of The Lost Mountains of northern Iowa are...

Question 2

A competitive firm produces its output according to the production function y = min{x^1/2, 10}.Let w be the price of the factor x, and let the price of output be $1.The demand for factor x, when the factor price is w, is

Accepted Answer

The firm will choose x to minimize cost while producing y = 10. The cost-minimizing x is found by setting x^1/2 = 10, giving x = 100. The demand for x is min{1/4w^2, 100} because the firm will use x = 100 if w is low enough, otherwise it will use less.

Question 3

A firm has the long-run cost function C(q)= 6q2 + 486.In the long run, it will supply a positive amount of output, so long as the price is greater than

Accepted Answer

The answer of A firm has the long-run cost function...

Question 4

A competitive firm produces its output according to the production function y = min{x2, 100}.Let w be the price of the factor x, and let the price of output be $1.The demand for x, when the price of x is w, is

Accepted Answer

The answer of A competitive firm produces its output according...

Question 5

A firm has the long-run cost function C(q)= 7q2 + 175.In the long run, it will supply a positive amount of output, so long as the price is greater than

Accepted Answer

In the long run, a firm will supply a positive amount of output if the price is greater than the minimum average cost. The given cost function is $C(q) = 7q^2 + 175$. To find the minimum average cost, we first find the average cost (AC) function by dividing the total cost by q: $AC = \frac{7q^2 + 175}{q} = 7q + \frac{175}{q}$. To find the minimum of this function, we take its derivative with respect to q and set it equal to zero: $AC' = 7 - \frac{175}{q^2} = 0$. Solving for q gives $q^2 = \frac{175}{7} = 25$, so $q = 5$. Substituting q = 5 back into the AC function gives the minimum average cost: $AC_{min} = 7(5) + \frac{175}{5} = 35 + 35 = 70$. Therefore, the firm will supply a positive amount of output as long as the price is greater than $70.

Question 6

A competitive firm produces its output according to the production function y = min{x3, 1000}.Let p be the price of output, and let the price of input x be $1.The profit maximizing output for this firm is

Accepted Answer

The answer of A competitive firm produces its output according...

Quiz 21: Firm Supply-Part A

A competitive firm produces its output according to the production function y = min{x^1/2, 10}.Let w be the price of the factor x, and let the price of output be $1.The demand for factor x, when the factor price is w, is

A firm has the long-run cost function C(q) = 6q2 + 486.In the long run, it will supply a positive amount of output, so long as the price is greater than

A competitive firm produces its output according to the production function y = min{x2, 100}.Let w be the price of the factor x, and let the price of output be $1.The demand for x, when the price of x is w, is

A firm has the long-run cost function C(q) = 7q2 + 175.In the long run, it will supply a positive amount of output, so long as the price is greater than

A competitive firm produces its output according to the production function y = min{x3, 1000}.Let p be the price of output, and let the price of input x be $1.The profit maximizing output for this firm is

Quiz 21: Firm Supply-Part A

A competitive firm produces its output according to the production function y = min{x1/2, 10}.Let w be the price of the factor x, and let the price of output be $1.The demand for factor x, when the factor price is w, is

A firm has the long-run cost function C(q) = 6q2 + 486.In the long run, it will supply a positive amount of output, so long as the price is greater than

A competitive firm produces its output according to the production function y = min{x2, 100}.Let w be the price of the factor x, and let the price of output be $1.The demand for x, when the price of x is w, is

A firm has the long-run cost function C(q) = 7q2 + 175.In the long run, it will supply a positive amount of output, so long as the price is greater than

A competitive firm produces its output according to the production function y = min{x3, 1000}.Let p be the price of output, and let the price of input x be $1.The profit maximizing output for this firm is

A competitive firm produces its output according to the production function y = min{x^1/2, 10}.Let w be the price of the factor x, and let the price of output be $1.The demand for factor x, when the factor price is w, is