Exam 21: Firm Supply-Part A

A firm's production function is f(x1, x2)= (min{x₁, 5x₂})^1/2.If the price of factor 1 is w1 = $5 per unit and the price of factor 2 is w2 = $25 per unit, then its supply function is given by the equation S(p)=

Price equals marginal cost is a sufficient condition for profit maximization.

A competitive firm has a long-run total cost function c(y)= 2y2 + 288 for y > 0 and c(0)= 0.Its long-run supply function is described as

A competitive firm is choosing an output level to maximize its profits in the short run.Which of the following is not necessarily true? (Assume that marginal cost is not constant and is well defined at all levels of output.)

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

Two firms have the same technology and must pay the same wages for labor.They have identical factories, but firm 1 paid a higher price for its factory than firm 2 did.If they are both profit maximizers and have upward-sloping marginal cost curves, then we would expect firm 1 to have a higher output than firm 2.

Mr.O.Carr has the cost function c(y)= y2 + 144 if his output, y, is positive and c(0)= 0.If the price of output is 18, Mr.Carr's profit-maximizing output is zero.

A competitive, capitalistic firm produces gift-wrapped pieces of the Berlin wall, using the standard Marxian inputs, K and L.The production function is y = (K + L)^1/2, where y is the number of pieces produced.Neglect the use of the wall itself.The price of capital, K, is r, and the price of labor, L, is w

A profit-maximizing firm continues to operate even though it is losing money.It sells its product at a price of $100.

A profit-maximizing dairy farm is currently producing 10,000 gallons of milk per day.The government is considering two alternative policies.One is to give the farm a lump sum subsidy of $500 per month.The other policy is to give the farm a subsidy of $.05 per gallon of output.

A firm faces competitive markets both for its inputs and its outputs.If its long-run supply curve is q = 3p,then it cannot have constant returns to scale.

A firm's production function is f(x1, x2)= (min{x₁, 4x₂})^1/2.If the price of factor 1 is w1 = $5 per unit and the price of factor 2 is w2 = $8 per unit, then its supply function is given by the equation S(p)=

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 uses two inputs and has a production function f(x1, x2)=23x.25 1x.25 2.The firm can buy as much of either factor as it likes at factor prices w1 = w2 = $1.The cost of producing y units of output for this firm is

A firm in a competitive industry takes account of the fact that the demand curve it confronts has a significant negative slope.

Suppose that Dent Carr's long-run total cost of repairing s cars per week is c(s)= 3s2 + 108.If the price he receives for repairing a car is $18, then in the long run, how many cars will he fix per week if he maximizes profits?

A competitive firm has a long-run total cost function c(y)= 3y2 + 675 for y > 0 and c(0)= 0.Its long-run supply function is described as

Irma's production function is f(x1, x2)=(min{x₁, 2x₂})^1/2.If the price of factor 1 is w1 = $3 and the price of factor 2 is w2 = $4, then her supply function is given by the equation

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?

Suppose that Dent Carr's long-run total cost of repairing s cars per week is c(s)= 3s2 + 75.If the price he receives for repairing a car is $18, then in the long run, how many cars will he fix per week if he maximizes profits?