ECON 3125 Exam 3

In the below table, the total cost of producing zero pizzas is shown to be equal to: Pizzas Fixed cost Variable cost Total cost Marginal Cost 0 $ $ $ $ 1 5 2 13 3 10 4 100 140 5 20 6 85 7 215

$100

The production manager of a clothing manufacturer estimates that the total annual cost of producing men's suits is given by the equation: TC = 5,000 + 4,100Q - 8Q^2 + .04Q^3 , At what output level does MC reach a minimum?

$100

In the short run, if average variable cost equals $50, average total cost equals $75, and output equals 100, the total fixed cost must be

$2,500

What is the total variable cost when output is 100 units?

$20,000

Plainco Corporation sells widgets for $3.00 each in market that is perfectly competitive. Increasing the number of Plainco workers from 1,000 to 1,001 would cause output to rise from 615 to 625 widgets per day. The marginal revenue product for the 1,001st worker is:

$30

If Total Cost: TC = 270 + 30Q + .3Q^2 What is the value of average variable cost at Q =2? What is the value of average fixed cost at Q = 2?

$30.6 $135 Total Cost: C(Q) = 270 +30Q + .3Q^2 Total Variable cost function: TVC(Q) = 30Q + .3Q^2 Average Variable cost function: AVC(Q) = (30Q + .3Q^2 )/Q = 30 + 0.3Q AVC(2) = 30 + 0.3(2) = 30.6 Total Fixed costs: TFC = 270 AFC = 270/Q => AFC(2) = 270/2 = 135

The production manager of a clothing manufacturer estimates that the total annual cost of producing men's suits is given by the equation: TC = 5,000 + 4,100Q - 8Q^2 + .04Q^3 . How much is AVC at an output of 100 units?

$3700

In the below Table, the variable cost of producing 4 pizzas is shown to be equal to: PizzasPizzas Fixed cost Variable cost Total cost Marginal Cost 0 $ $ $ $ 1 5 2 13 3 10 4 100 140 5 20 6 85 7 215

$40

John graduates from UNC Charlotte with an accounting degree. He turns down a $40,000 per year accounting job to open a bicycle repair shop. He repairs the bikes himself and makes an annual profit of $50,000. What is the true "profit" he has made by deciding to open the bicycle shop? What is his accounting profit? Economic profit?

$50,000; $10,000

The total fixed cost for the firm is:

$500

DigiWatch plans to open a new production facility to produce digital watches. The fixed costs of the plant will be $366,000 per year, and that average variable cost will be: AVC = 7 + 0.002 Q. What is the average cost for the first year of production at an output of 6,000 watches?

$80

Refer to the above figure, what is the total fixed cost?

$9600

Marginal revenue product of labor (MRPL) equation:

(MR)(MPL)

Your firm's the production function: Q = 4K^1/2*L^1/2 Suppose that the price of labor is $5 per person hour and the price of capital is $20 per machine hour. Given a budget of $100, how many labor hours should your firm employ to produce the maximum output?

10

Differentiate the equation: Q = 10 L - 0.5 L^2 + 24 K - K^2, in terms of MPl

10-L

A firm produces according to the production function: Q = K0.5L0.5 where Q = units of output, K = units of capital, and L = units of labor. In the short run, the firm has a fixed amount of capital, K =9. How many L it takes produce an output of 12?

16

Making dresses is a labor-intensive process. Indeed, the production function of a dressmaking firm is well described by the equation Q = L - L^2/800, where Q denotes the number of dresses per week and L is the number of labor hours per week. The firm faces the fixed selling price, P = $40. The firm's additional cost of hiring an extra hour of labor is about $20 per hour (wage plus fringe benefits). How much labor should the dress maker employ?

200

Differentiation the equation: Q = 10 L - 0.5 L^2 + 24 K - K^2, in terms of MPk

24-2K

Suppose the production function is Q = min {2K, L}. How much output is produced when 4 units of labor and 9 units of capital are employed?

4

Making dresses is a labor-intensive process. Indeed, the production function of a dressmaking firm is well described by the equation Q = L - L^2/800, where Q denotes the number of dresses per week and L is the number of labor hours per week. The firm faces the fixed selling price, P = $40. The marginal revenue product of labor is:

40 - (0.1L)

Davy Metal Company produces brass fittings. Davy's engineers estimate the production function represented below as relevant for their long-run capital-labor decisions. Q = 500L^0.6K^0.8 where Q = annual output measured in pounds, L = labor measured in person hours, K = capital measured in machine hours. Davy's employees are relatively highly skilled and earn $15 per hour. The firm estimates a rental charge of $50 per hour on capital. Given a $350,000 budget, how many machine hours should the firm employ?

4000

Differentiate the equation Q = 500L^.8*K^.6 in terms of MPl and MPk

400L^-.2*K^.6 300L^.8*K^-.4

The below table shows the change in the production of pizzas as more workers are hired. The marginal product of the second employee equals: Production of Pizza data Workers Pizzas 0 0 1 4 2 10 3 15 4 18 5 19

6

As more output is produced, AFC ___:

AFC decreases throughout the range of output.

TC = 1000 + 174Q -4Q^2 + Q^3 •Derive the AVC function? •Derive the MC function? •How much is AVC at an output of 10 units? At what output level does AVC reach a minimum? At what output level does MC reach a minimum? Illustrate with AVC-MC diagram

AVC = 174 - 4Q + Q^2 MC = 174 - 8Q + 3Q^2 AVC(10) = $234 Q = 2 Q=1.33

Hideki is the owner/operator of Hideki's Flower Shop. Last year he earned $100,000 in total revenue. His explicit costs were $60,000 paid to his employees and suppliers (assume that this amount represents the total opportunity cost of these resources). During the course of the year he received three offers to work for other flower shops with the highest offer being $60,000 per year. Calculate Hideki's accounting and economic profit.

Accounting profit = $40,000; economic profit = negative $20,000.

What is the marginal product of labor equation?

Change in Q/ Change in L

If a firm's production function is Q = 3.25 L0.50K0.25 then the production has

Decreasing returns to scale

Accounting costs and economic costs differ because:

Economic costs include implicit costs and accounting costs do not.

Marginal cost of labor (MCL ) equation:

MCL = ΔTLC/ΔL

If Q = 500L^.6*K^.8, them which of the following is true?

MPk = 400L^.6*k^-.2

If Q = 5L+6LK^2+8K, then which of the following is true?

MPl = 5+6K^2

Profit-maximization hiring rule:

MRPl = MCl

Marginal - Average Rule

Marginal - Average Rule If MC > AVC , AVC is rising If MC < AVC, AVC is falling If MC = AVC, AVC is at its minimum

In the short run, is it possible for a firm to change inputs?

Not completely, one or more inputs are fixed.

The Law of Diminishing Marginal Returns:

Principle that says as the use of an input increases with other inputs fixed, a point will be reached beyond which total product will increase at a decreasing rate, i.e. marginal product of the variable input will decline

If TC = 270 + 30 Q + 0.3 Q^2 What level of Q generates the minimum average cost? What is the value of ATC at this Q?

Q = 30 $48 Reason: ATC = TC/Q = 270/Q + 30 + .3Q Set MC = ATC => 30 + 0.6Q = 270/Q + 30 + .3Q => 270/Q = 0.3Q => Q^2 = 900 => Q = 30 ATC = 270/Q + 30 + .3Q = 270/30 + 30 + 0.3(30) = $48

What are the two major concerns of managerial decision making?

Revenue enhancement and cost control

Equations to learn:

TC = TVC + TFC -Average Total Cost ATC = TC/Q ATC = AVC + AFC -Average Variable Cost AVC = TVC/Q -Average Fixed Cost AFC =TFC/Q

increasing returns to scale:

a given % change in all inputs results in a greater % change in output

constant returns to scale

a given % change in all inputs results in an equal % change in output

What is short-run?

a period of time in which the amount of one or more of the inputs cannot be changed

What is long-run?

a period of time sufficiently long to allow the firm to vary all of its inputs.

Variable inputs are defined as any resource that:

can be changed as output changes.

Marginal revenue product of labor (MRPL) is defined as

change in total revenue divides by change in labor.

AFC ___ as output increases.

decreases

AVC, ATC and MC ___ as output increases.

decreases and then increases

An auto parts manufacturer hires 10 works and uses 10 machines to produce 93 units of auto parts. If the manufacturer doubles both the amounts of workers and machines,180 units of auto parts are produced. We can conclude that the production function exhibits________ and the long-run average total cost is_______.

decreasing returns to scale; increasing

Q = 10 L - 0.5 L2 + 24 K - K2 ¡The price of labor is $10, the price of K is $10 returns to scale is?? ATC is increasing, decreasing or remains constant?? Conclusion: ____ returns to scale and ATC is ____.

decreasing; rising

If a firm's long-run average cost curve is rising, it is experiencing:

diseconomies of scale

For constant returns to scale, the output elasticity is ___?

equal to one

Total Fixed Costs (TFC):

expenditures spent on fixed input ex. rent on production plant the cost of equipment

Total variable costs

expenditures spent on variable inputs

decreasing returns:

given % change in all inputs results in a smaller % change in output

For increasing returns to scale, the output elasticity is ___?

greater than one

When the MP of labor is positive, then total output ____?

increases

•TC ___ as output increases. However, it first increases at decreasing rate and then increases at increasing rate. At zero output, TC is equal to ___.

increases; TFC

•TVC ___ as output increases. However, it first increases at decreasing rate and then increases at increasing rate. At zero output, TVC is ___.

increases; zero

If the objective of the firm is to maximize profit, the firm must balance:

input productivity and input costs

Fixed inputs are:

inputs that cannot be changed in the short run

Variable inputs are:

inputs the manager can adjust to alter production

If MRPL < MCL, the firm should hire:

less

For decreasing returns to scale, the output elasticity is ___?

less than one

disEconomies of Scale Basic points: double all inputs, output ___ than doubled or it takes ___ than double amount of inputs to produce ___ of output. average cost per unit of output ___ as the firm increases output. examples?? When a firm becomes too large, bureaucratic red tape, or breakdown in communication flows tend to rise.

less; more; double amount; increases

The law of diminishing returns occurs with each additional unit of a variable input when:

marginal product of the variable input begins to decline.

If MRPL > MCL, the firm should hire:

more

Economies of Scale Basic points: double all inputs, output ___ than doubled or it takes ___ than double amount of inputs to produce ___ of output. average cost per unit of output ___ as the firm increases output. examples?? A large hospital producing patient services at lower cost than smaller hospital because a large hospital can spread fixed cost over a larger number of patients

more; less; double amount; decreases

Marginal cost refers to additional cost of producing___.

one more unit of output

When the MP of labor is zero, then total output ____?

reaches maximum

•TFC ___ as output increases. Also, TFC has to be paid even if output is zero.

remains changed

If the marginal cost curve is above the average variable cost curve, the average variable cost must be

rising

If marginal labor cost > marginal revenue product of labor, then the firm:

should hire less labor

A firm's production function:

shows the maximum output the firm can produce for any combination of inputs.

Marginal product is:

the additional output produced by an additional unit of an input, holding other inputs fixed.

Returns to scale:

the percentage change in output resulting from a given percentage change in inputs

When all inputs are variables:

total costs = variable costs

Total product is:

total output by using units of inputs

How is revenue enhanced?

understand consumer behavior and estimate demand

How is cost controlled?

understand cost behavior, the components of cost: TVC, TFC,.... & estimate cost