What is the profit maximizing level of output for a firm with the marginal cost function MC

What is the profit maximizing level of output for a firm with the marginal cost function MC = 1.6Q²-15Q+60 and a marginal revenue function MR = 280-20Q?

Solutions

Expert Solution

Profit is maximized where;

Marginal revenue (MR) = Marginal cost (MC)

280-20Q = 1.6Q²-15Q+60

1.6Q²+5Q-220=0

Using quadratic formula to solve for Q

a=1.6, b=5, c=-220

There cannot be can’t have negative output.

Therefore, Profit maximising level of output is Q = 10.27.

There cannot be can’t have negative output. Therefore, Profit maximising level of output is Q = 10.27.

Joes answered 2 years ago

Next > < Previous

Related Solutions

If a profit-maximizing firm is producing an output level in which marginal revenue exceeds marginal cost,...

If a profit-maximizing firm is producing an output level in which marginal revenue exceeds marginal cost, should it produce more, less or the same? Why? What is the profit-maximizing quantity for any firm to produce?

Why is the level of output at which marginal revenue equals marginal cost the profit maximizing...

Why is the level of output at which marginal revenue equals marginal cost the profit maximizing output?

For competitive firms, they set marginal cost equal to market price at profit-maximizing level of output....

For competitive firms, they set marginal cost equal to market price at profit-maximizing level of output. In the short run, marginal revenue curve faced by a competitive firm is downward-sloping. Competitive firms always produce a positive amount of output in the short run (q > 0). Competitive firms earn zero economic profit in the long run equilibrium. All these are True False Questions

A competitive firm has a marginal cost equal to: MC(y)=3y, where y is the output level....

A competitive firm has a marginal cost equal to: MC(y)=3y, where y is the output level. The intersection of the average cost and the marginal cost happens at output level equal to 4. How much will the firm produce in the long-run at price equal to $9?

The marginal cost of the production is always 13.00 and the profit maximizing output, average a total cost is $20.00

The following table shows a demand schedule facing a monopolist. Quantity: 0 1 2 3 4 5 6 7 8 9 10 Prices: 25 25 24 23 22 21 20 19 18 17 16 The marginal cost of the production is always 13.00 and the profit maximizing output, average a total cost is $20.00 What is the profit maximizing (or loss minimizing) output for this? What is the price at which that output will sell in the market? Compute the...

The firm has the following marginal cost function: MC(y) = 3 + .25y what is the...

The firm has the following marginal cost function: MC(y) = 3 + .25y what is the change in producer surplus when the price of y changes from $ 20 to $ 50?

At the current level of output, a profit-maximizing firm in a competitive market earns average revenue...

At the current level of output, a profit-maximizing firm in a competitive market earns average revenue of $25, has an average total cost of $22 and an average variable cost of $17. If the firm's marginal cost curve is equal to its average total cost curve at an output level of 20,000 units, then the firm earns profit of $60,000 at its current level of output. True False The short-run supply for a firm in a perfectly competitive market will...

1. The Profit-maximizing Level of output for a perfectly competitive firm in the short run occurs...

1. The Profit-maximizing Level of output for a perfectly competitive firm in the short run occurs where: a. marginal revenue equals price B. Total revenue equals total cost C.marginal cost equals price D. Average revenue equals average total cost 2. Marginal revenue is a firms: A. Ratio of the change in total revenue to change in output. B. Profit per unit times the number of units sold C. Ratio of average revenue to total revenue D. Increase in profit when...

A profit-maximizing competitive firm has the production function ? = ?^.25?^.25 , where output ? is...

A profit-maximizing competitive firm has the production function ? = ?^.25?^.25 , where output ? is produced using capital (?) and labor (?). The price of labor is $2 and the price of capital is $6. The price of the firm’s output is $100. a. Write the firm’s profit function and calculate the first-order conditions. Provide an economic interpretation for each of the first-order conditions. b. Find the profit-maximizing quantities ?* and ?*. c. Find the firm’s total costs. d....

a. If the marginal revenue is less than the marginal cost, what should a profit-maximizing company...

a. If the marginal revenue is less than the marginal cost, what should a profit-maximizing company do? b. In a perfectly competitive graph, how does one calculate the economic profit? c. What is the shutdown point in a perfectly competitive firm? ' d. Briefly, what is the difference between economies of scale and diseconomies of scale? Why is it important to the firm? e. Given the following total cost function TC(q) = 1000 + 13q. Find the fixed cost, variable...

Subjects