Exam 18: Profit Maximization

A competitive firm uses a single input x to produce its output y. The firm's production function is given by y = for quantities of x between 0 and 4. For quantities of a greater than 4, the firm's output is y = 4 + x. If the price of the output y is $1 and the price of the input x is $3, how much x should the firm use to maximize its profit?

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

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 $700 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 $400 per week, the business's economic profits are

A competitive firm produces a single output using several inputs. The price of output rises by $4 per unit. The price of one of the inputs increases by $4 and the quantity of this input that the firm uses increases by 16 units. The prices of all other inputs stay unchanged. From the weak axiom of profit maximization we can tell that

If the short-run marginal costs of producing a good are $40 for the first 200 units and $50 for each additional unit beyond 200, then in the short run, if the market price of output is $46, a profit-maximizing firm will

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.

A competitive firm produces output using three fixed factors and one variable factor. The firm's short-run production function is q = 154x - 5x², where x is the amount of variable factor used. The price of the output is $2 per unit and the price of the variable factor is $8 per unit. In the short run, how many units of x should the firm use?

A competitive firm produces a single output using several inputs. The price of output rises by $3 per unit. The price of one of the inputs increases by $6 and the quantity of this input that the firm uses increases by 12 units. The prices of all other inputs stay unchanged. From the weak axiom of profit maximization we can tell that

The production function is given by F(L) = . Suppose that the cost per unit of labor is $16 and the price of output is $12. How many units of labor will the firm hire?

If the value of the marginal product of factor x increases as the quantity of x increases and the value of the marginal product of x is equal to the wage rate, then the profit-maximizing amount of x is being used.

A competitive firm produces output using three fixed factors and one variable factor. The firm's short-run production function is q = 524x - 4x², where x is the amount of variable factor used. The price of the output is $3 per unit and the price of the variable factor is $12 per unit. In the short run, how many units of x should the firm use?

If the price of the output of a profit-maximizing, competitive firm rises and all other prices stay constant, then the firm's output cannot fall.