Exam 20:Profit Maximization-Part A

Just as in the theory of utility-maximizing consumers,the theory of profit-maximizing firms allows the possibility of Giffen factors.These are factors for which a fall in price leads to a fall in demand.

A competitive firm's production function is f(x₁,x₂)=6x^1/2₁+8x^1/2₂.The price of factor 1 is $1 and the price of factor 2 is $4.The price of output is $8.What is the profit-maximizing quantity of output?

During the height of the pet rock craze in the 1970s,the price elasticity of demand was estimated to be 1.20.Since pet rocks have a marginal cost of zero,a profit-maximizing seller of pet rocks would

A competitive firm has a production function described as follows."Weekly output is the square root of the minimum of the number of units of capital and the number of units of labor employed per week." Suppose that in the short run this firm must use 16 units of capital but can vary its amount of labor freely. a.Write down a formula that describes the marginal product of labor in the short run as a function of the amount of labor used.(Be careful at the boundaries. ) b.If the wage is w = $1 and the price of output is p =$4,how much labor will the firm demand in the short run? c.What if w = $1 and p = $10? d.Write down an equation for the firm's short-run demand for labor as a function of w and p.

The marginal product of a factor is just the derivative of the production function with respect to the amount of this factor,holding the amounts of other factor inputs constant.

Jiffy-Pol Consultants is paid $1,000,000 for each percentage of the vote that Senator Sleaze receives in the upcoming election.Sleaze's share of the vote is determined by the number of slanderous campaign ads run by Jiffy-Pol according to the function S=100N/(N + 1),where N is the number of ads.If each ad costs $3,600 approximately how many ads should Jiffy-pol buy in order to maximize its profits?

During the height of the pet rock craze in the 1970s,the price elasticity of demand was estimated to be 1.20.Since pet rocks have a marginal cost of zero,a profit-maximizing seller of pet rocks would

A fixed factor is a factor of production that is used in fixed proportion to the level of output.

A competitive firm's production function is f(x₁,x₂)=12x^1/2₁ +4x^1/2₂.The price of factor 1 is $1 and the price of factor 2 is $2.The price of output is $4.What is the profit-maximizing quantity of output?

A firm produces one output using one input.When the cost of the input was $3 and the price of the output was $3,the firm used 6 units of input to produce 18 units of output.Later,when the cost of the input was $7 and the price of the output was $4,the firm used 5 units of input to produce 20 units of output.This behavior

When Farmer Hoglund applies N pounds of fertilizer per acre,the marginal product of fertilizer is 1 =N/100 bushels of corn.If the price of corn is $2 per bushel and the price of fertilizer is $40 per pound,then how many pounds of fertilizer per acre should Farmer Hoglund use in order to maximize his profits?

Diesel Dan is a contract truck driver.While his revenue is $1.50 per mile driven,the faster he drives,the greater the risk of a speeding ticket.The cost of driving his truck 1 hour at a speed of S miles per hour is C(S)= e^{S - (60/4)}.To maximize his profit,Dan should drive

The production function is given by f(x)=4x^1/2.If the price of the commodity produced is $80 per unit and the cost of the input is $40 per unit,how much profits will the firm make if it maximizes profits?

During the height of the pet rock craze in the 1970s,the price elasticity of demand was estimated to be 1.80.Since pet rocks have a marginal cost of zero,a profit-maximizing seller of pet rocks would

The production function is given by f(x)= 4x^1/2.If the price of the commodity produced is $60 per unit and the cost of the input is $10 per unit,how much profit will the firm make if it maximizes profits?

Philip owns and operates a gas station.Philip works 40 hours a week managing the station but doesn't draw a salary.He could earn $800 a week doing the same work for Terrance.The station owes the bank $100,000 and Philip has invested $100,000 of his own money.If Philip's accounting profits are $1,000 per week while the interest on his bank debt is $300 per week,the business's economic profits are

The production function is given by F(L)=6L^2/3.Suppose that the cost per unit of labor is $16 and the price of output is $16.How many units of labor will the firm hire?

If the value of the marginal product of labor exceeds the wage rate,then a competitive,profit-maximizing firm would want to hire less labor.

Diesel Dan is a contract truck driver.While his revenue is $2 per mile driven,the faster he drives,the greater the risk of a speeding ticket.The cost of driving his truck 1 hour at a speed of S miles per hour is C(S)= e^{S - (60/5)}.To maximize his profit,Dan should drive

If there is perfect certainty,a competitive firm will necessarily