Question 1

-At Albert's Pretzel Company,MPL = 1/L,and MPK = 1/K.The isoquant for 100 pounds of pretzels daily is shown in the above figure.Albert minimizes the cost of producing 100 pounds of pretzels daily by hiring five units of labor and 10 units of capital when w = 50 and r = 25.When r rises to 100,what is the minimum cost of producing 100 pounds of pretzels daily in the short run? in the long run?

Accepted Answer

The answer of 
-At Albert's Pretzel Company,MPL = 1/L,and MPK...

Question 2

For the following, please answer "True" or "False" and explain why.
-Short-run average cost exceeds long-run average cost only when there are economies of scale.

Accepted Answer

Short-run average costs exceed long-run average costs because the firm is locked into a certain input mix in the short run that may not be cost minimizing when all inputs are variable.This condition holds regardless of the presence of economies of scale.

Question 3

Suppose Ralph hires workers at his supermarket at a wage of $12/hour.Ralph currently has 10 checkstands (i.e.,capital)with a rental rate of $10/hour.Production of customers served (i.e.,output)is determined by the hourly production function
f(L,K)= 0.5L³/⁴ᴷ²
For the questions that follow,the number of checkstands is fixed.Show your work clearly.
a.If Ralph wants to serve 400 customers per hour,how many workers must he employ? How much will it cost to serve 400 customers per hour?
b.Derive Ralph's short-run cost function with the 10 checkstands.
c.Derive the equations for the MC,AC,AVC,and AFC.

Accepted Answer

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Question 4

A firm currently employs five units of capital.When the firm adds a sixth unit of capital,it is able to reach a lower average cost for a greater quantity of output.What does this tell you about the shape of the long-run average cost curve and are economies of scale occurring? Explain briefly.Does this necessarily imply increasing or decreasing returns to scale in production or is it ambiguous? Explain briefly.

Accepted Answer

The answer of A firm currently employs five units of...

Question 5

For the following, please answer "True" or "False" and explain why.
-Short-run costs are never equal or lower than long-run cost.

Accepted Answer

Since the long-run curve "envelopes" all short-run curves there is always a level of output where short-run cost are equal to long-run cost.However,short-run cost can never be lower than long-run cost.

Question 6

Long-run average cost is never greater than short-run average cost because in the long run

Accepted Answer

In the long run, the firm has more flexibility in adjusting its inputs and can move to the lowest possible isocost curve. This means that it can achieve a lower average cost than what is possible in the short run. Therefore, long-run average cost is never greater than short-run average cost.

Question 7

After 2 years of operation,the workers in XYZ Co.become more adept because of their repeating work.As a result,the average cost of production is lowered due to

Accepted Answer

The phrase "workers in XYZ Co. become more adept because of their repeating work" suggests that they are learning by doing, a concept commonly used in economics. This means that as workers repeat the same task, they become better at it, which leads to greater efficiency and productivity. This process is associated with decreasing average costs and is referred to as learning by doing. Therefore, the best choice is D - learning by doing.

Question 8

Which of the following statements best explains why long-run average cost is never greater than short-run average cost?

Accepted Answer

In the long run, firms have the flexibility to adjust their inputs and take advantage of economies of scale. This means that they can achieve a tangency of the isocost and isoquant curves, which minimizes their costs. In the short run, however, firms are constrained by their fixed inputs, and may experience diminishing returns or other short-run inefficiencies. Therefore, long-run average cost is never greater than short-run average cost.

Question 9

Explain why in the long run a firm that is cost minimizing will choose K and L where:
w/MPL = r/MPK
What does this tell you about the marginal cost of increasing output through hiring labor and the marginal cost of increasing output through adding capital?

Accepted Answer

The answer of Explain why in the long run a...

Question 10

Determine the output expansion path (equation)for a cobb-douglas production function f(L,K)= 10LᵃK¹⁻ᵃ.How does the shape of the output expansion path change as "a" changes?

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The answer of Determine the output expansion path (equation)for a...

Question 11

Joey notices that by employing an additional hairdresser,he will be able to increase the number of haircuts in his salon by 15 haircuts per day.The daily salary he will need to pay the hairdresser is $200.How much is the cost for an additional haircut? Describe the general relationship between the marginal product and marginal cost curves.

Accepted Answer

The answer of Joey notices that by employing an additional...

Question 12

Sam and Erica are starting a new restaurant in Portland,Oregon.While Sam plans to do the cooking himself,he will need to employ workers and machinery to produce food.He estimates his production function as:
q = 15L.²⁵K
Sam is able to accumulate $10,000 to finance the business.Workers cost $10 and capital costs $50.
a.If Sam wishes to produce the most output with the finances available,how much labor and capital should Sam employ? Use a Lagrangian to solve this problem.
b.Does this bundle of capital and labor also minimize the costs? Explain using a graph.

Accepted Answer

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Question 13

Sam's company produces output with labor and capital.At the current quantities of labor and capital,the following information is obtained: the output produced by spending one more dollar on labor exceeds the output produced by spending one more dollar on capital.In the long run,is Sam minimizing costs? If not,explain how capital and labor should change (holding output constant)and how this relates to the MRTS = w/r condition.

Accepted Answer

The answer of Sam's company produces output with labor and...

Question 14

In the long run,the expansion path is

Accepted Answer

The answer of In the long run,the expansion path is
...

Question 15

This question has you determine the effect of a tax on labor on the long-run cost function.Consider a firm with the production function f(L,K)= LK.The wage rate and rental rate on capital are w and r,respectively.
a.Using the Lagrangian,derive the long-run cost function for this firm.
b.Suppose the government taxes labor at by an amount t per unit of labor.Rewrite the long-run cost function including the tax.Hint: the effective wage rate is now w + t.
c.Compute the marginal effect of the tax on the long-run cost function.To do so,compute the partial derivative of the cost function with respect to t.Does an increase in the tax increase the cost linearly?

Accepted Answer

The answer of This question has you determine the effect...

Question 16

Learning by doing will result in

Accepted Answer

Learning by doing results in the accumulation of knowledge and experience, which leads to improved efficiency and lower costs in the long run compared to the short run. This is due to the fact that in the short run, firms may have to undertake more costly trial and error methods to learn, whereas in the long run they will have already learned what works best and can implement it more efficiently. Thus, long-run costs will be lower than short-run costs.

Question 17

In the short run,the expansion path is

Accepted Answer

In the short run, the expansion path is horizontal because the firm can only adjust variable inputs while fixed inputs remain constant, leading to changes in output levels along a horizontal path.

Question 18

To dig a trench,each worker needs a shovel.Workers can only use one shovel at a time.Workers without shovels do nothing,and shovels cannot operate on their own.What kind of production technology is this? Graphically (with isocost and isoquant lines)determine the optimal number of shovels and workers used by a firm to dig two trenches when w = r = 10.What will be the (long-run)total cost of the two trenches? What will happen if the rental rate drops to $5 while the wage remains at $10? Add the relevant lines to your graph and compute the new optimal quantity of inputs and total cost.

Accepted Answer

The answer of To dig a trench,each worker needs a...

Question 19

A paper company dumps nondegradable waste into a river that flows by the firm's plant.The firm estimates its production function to be:
Q = 6KP,
where Q = annual paper production measured in pounds,K = machine hours of capital,and P = gallons of polluted water dumped into the river per year.The firm currently faces no environmental regulation in dumping waste into the river.Without regulation,it costs the firm $7.50 per gallon dumped.The firm estimates a $30 per hour rental rate on capital.The firm produces 600 million pounds of paper per year.For this problem,consider the long-run production of output.
a.Determine the firm's optimal ratio of wastewater to capital.
b.Given the firm's output of 600 million lbs,how much capital and wastewater should the firm employ?
c.How much will it cost the firm to produce the 600 million lbs of paper?
d.The state environmental protection agency plans to impose a $7.50 fee for each gallon that is dumped (this is in addition to the current cost of $7.50).Assuming that the firm intends to maintain its same output level,how much capital and wastewater should the firm employ?
e.How much will the firm pay in fees? What happens to the firm's cost as a result of the fee?

Accepted Answer

The answer of A paper company dumps nondegradable waste into...

Question 20

What is the last dollar rule for cost-minimization? Provide a brief explanation (in words)as well as the corresponding mathematical equality.If the firm is producing at a point where the isocost line is steeper than the isoquant,what does the last dollar rule imply (i.e.,where is the last dollar most productive,L or K)and how should the firm alter its capital and labor in the long run?

Accepted Answer

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Quiz 7: Costs

For the following, please answer "True" or "False" and explain why. -Short-run average cost exceeds long-run average cost only when there are economies of scale.

For the following, please answer "True" or "False" and explain why. -Short-run costs are never equal or lower than long-run cost.