Homework in mangerial economics - Assignment Example

Suppose that the total cost curve for your company is given by: a) What is the marginal cost curve? SOLUTION b) What is the average cost curve? What is the average cost of producing 100 units? SOLUTIONc) If the price of a unit of output is $40 independent of the quantity produced how many units must your company sell to break even? SOULTION2. For each of the following production functions, does the function exhibit constant, increasing, or decreasing returns to scale:a) SOLUTIONLet’s first calculate the marginal products and check whether they are diminishing, constant, or increasing.

For the MRTS we get MRTS . Checking for returns to scale (we are scaling up all inputs for a factor t > 1):So, this production function exhibits increasing returns to scaleb) SOLUTIONLet’s first calculate the marginal products and check whether they are diminishing, constant, or increasing. For the MRTS we get MRTS . Checking for returns to scale (we are scaling up all inputs for a factor t > 1):So, this production function exhibits increasing returns to scalec) SOLUTIONLet’s first calculate the marginal products and check whether they are diminishing, constant, or increasing.

For the MRTS we get MRTS . We verify constant returns to scale:So, this production function exhibits constant returns to scale3. You estimate that your company has the following daily production function:Where is the number of hours of skilled labor and is the number of hours of unskilled labor. a) Suppose the wage for skilled labor is $20 per hour and the wage for unskilled labor is $10 per hour. If you are the owner of the company how would you evaluate the suggestion of the manager that you should hire 100 hours of skilled labor and 50 hours of unskilled labor?SOLUTIONb) If the price of a unit of output is $5 independent of the quantity produced how many units of skilled labor should you hire?4. The White Company is a member of the lamp industry, which is perfectly competitive.

The price of the lamp is $50. The firm’s total cost function is;Where TC is the total cost (in dollars) and Q is hourly output.a) What output maximizes profit?b) What is the firm’s economic profit at this output?SOLUTION Price associated with Q=3 is;So the firm’s profit is;c) What is the firm’s average cost at this output?SOLUTIONd) If other firms in the lamp industry have the same cost function as this firm, is the industry in equilibrium? Why or why not?6. The Deering manufacturing company’s short-run average cost function in 2012 was Where AC is the firm’s average cost (in dollars per pound of the product) and Q is its output rate.a) Obtain an equation for the firm’s short-run total cost functionSOLUTIONb) Does the firm have any fixed costs?

Explain c) If the price of the Deering manufacturing company’s product (per pound) is $3, is the firm making profit or loss? Explaind) Derive an equation for the firm’s marginal cost?SOLUTION7. The Smith Company made and sold 10,000 metal tables last year. When output was between 5000-10,000 tables, its average cost was $24. In this output range, each table contributed 60% of its revenue to fixed costs and profit.a) What was the price per table?SOLUTION b) If the Smith company increases its price by 10%, how many tables will it have to sell next year to obtain the same profit as last year?SOLUTIONd) If the Smith company increases its price by 10%, and its variable cost increases by 10% as a result of wage increases, how many tables will the firm have to sell next year to have the same profit as last year?SOLUTION8. Suppose that the total cost curve for your company is given by: a) What is the marginal cost curve?

SOLUTIONb) If the firm is in a perfectly competitive and the price of the good is $32, what is the optimal output? SOLUTIONSince the firm is producing in a perfectly competitive market, the firm views the output price as exogenous. It should produce up to the point at which , that is, c) At this output, what is your profit? SOLUTIONPrice associated with Q=7 units is;So the firm’s profit is;