Question

In: Economics

SuperiorSharp Inc. produces scissors. Wages are $12 per hour and all the scissors-making equipment rents for...

SuperiorSharp Inc. produces scissors. Wages are $12 per hour and all the scissors-making equipment rents for a total of $36 per hour. The production function is Q = 30K0.75L0.25, where K and L denote its capital and labor inputs, respectively.

a.   The firm is currently producing 3000 pairs of scissors and has determined (correctly) that the cost-minimizing quantities of labor and capital are 100 units of labor and 100 units of capital. Sketch this equilibrium, using isoquants and isocost lines, and label it A.

b.   The firm now wants to increase output to 4200 pairs of scissors. If capital is fixed at K = 100 in the short run, how much additional labor will the firm require? Sketch in the new short run equilibrium on your graph, and label it B. How much does it cost the firm to produce 4200 pairs of scissors in the short run?

c.   Find the optimal level of capital and labor required to produce 4200 pairs of scissors in the long run, and add the new long run equilibrium to your graph, labeling it C. How much will it now cost to produce 4200 pairs of scissors? Explain.

Solutions

Expert Solution

(a)

In following graph, initial equilibrium is at point A where isoquant Q0 is tangent to isocost line C0 with optimal input mix being (K0= 100, L0 = 100).

(b)

When K = 100 and Q = 4200,

30 x (100)0.75 x L0.25 = 4200

(100)0.75 x L0.25 = 140

L0.25 = 4.43

L = 384.16

Increase in L = 284.16 - 100 = 284.16

Total cost = wL + rK = 12 x 384.16 + 36 x 100 = 4609.92 + 3600 = 8209.92

In above graph, short run equilibrium is at point B where new isocost Q1 is tangent to C0 with new input mix being (K0 = 100, L1 = 384.16)

(c)

Cost is minimized when MPL/MPK = w/r = 12/36 = 1/3

MPL = Q/L = 30 x (K/L)0.75

MPK = Q/K = 30 x (L/K)0.25

MPL/MPK = K/L = 1/3

L = 3K

Plugging in production function,

30 x (K)0.75 x (3K)0.25 = 4200

30.25 x (K)0.75 x K0.25 = 140

K = 106.38

L = 3 x 106.38 = 319.14

Total cost = 12 x 319.14 + 36 x 106.38 = 3829.68 + 3829.68 = 7659.36

In above graph, long run equilibrium is at point C where new isocost Q1 is tangent to new isocost line C1 with new input mix being (K1 = 106.38, L2 = 319.14).

Rahul Sunny answered 2 years ago
Next > < Previous

Related Solutions

Economists would argue that all per-hour wages could be the same for everyone if four conditions...
Economists would argue that all per-hour wages could be the same for everyone if four conditions (or compensating differentials) are met. Unfortunately none of those conditions are met in reality. Let's assume you are a policy maker that cares that everyone has equal access to wages. Specifically answer this prompt: Pick one of the four main conditions and craft a policy that may help to make the condition apply to reality. The four conditions: The demand for every type of...
Economists would argue that all per-hour wages could be the same for everyone if four conditions...
Economists would argue that all per-hour wages could be the same for everyone if four conditions are met. Unfortunately none of those conditions are met in reality. Let's assume you are a policy maker that cares that everyone has equal access to wages. Specifically answer this prompt: Pick one of the four main conditions and craft a policy that may help to make the condition apply to reality. The four conditions: The demand for every type of labor is the...
It is assumed that there is an average of 12 customers per hour at a service...
It is assumed that there is an average of 12 customers per hour at a service counter according to a Poisson process. a) How likely is it that 4 customers show up at this counter in the next 15 minutes? b) Given that 4 customers showed up at this counter in a given 15-minute period, what is the probability that there were at least 2 customers that showed up in the last 5 minutes of this period?
Stark Company has five employees. Employees paid by the hour receive a $12 per hour pay...
Stark Company has five employees. Employees paid by the hour receive a $12 per hour pay rate for the regular 40-hour workweek plus one and one-half times the hourly rate for each overtime hour beyond the 40 hours per week. Hourly employees are paid every two weeks, but salaried employees are paid monthly on the last biweekly payday of each month. FICA Social Security taxes are 6.2% of the first $118,500 paid to each employee, and FICA Medicare taxes are...
12. The per-unit standards for direct labor are 1.5 direct labor hours at $15 per hour....
12. The per-unit standards for direct labor are 1.5 direct labor hours at $15 per hour. If in producing 3400 units, the actual direct labor cost was $69750 for 4500 direct labor hours worked, the total direct labor variance is $2250 unfavorable. $6750 unfavorable. $6750 favorable. $3400 unfavorable. 13. A company purchases 10000 pounds of materials. The materials price variance is $7000 favorable. What is the difference between the standard and actual price paid for the materials? $1.43 $0.70 $7.00...
Using the midpoint method, the elasticity of Cho's labor supply between the wages of $50 and $65 per hour is approximately
Calculating the price elasticity of supply Cho is a retired teacher who lives in Dallas and does some consulting work for extra cash. At a wage of SSO per hour, she is willing to work iO hours per week. At $65 per hour, she is willing to work 19 hours per week. Using the midpoint method, the elasticity of Cho's labor supply between the wages of $50 and $65 per hour is approximately _______ . which means that Cho's supply of labor...
Using the midpoint method, the elasticity of Amy's labor supply between the wages of $25 and $40 per hour is approximately
6. Calculating the price elasticity of supply Amy is a stay-at-home parent who lives in Dallas and provides math tutoring for extra cash. At a wage of $25 per hour, she is willing to tutor 4 hours per week. At $40 per hour, she is willing to tutor 10 hours per week. Using the midpoint method, the elasticity of Amy's labor supply between the wages of $25 and $40 per hour is approximately _______ ,which means that Amy's supply of labor over...
An individual can earn $12 per hour if he or she works. There are 30 days...
An individual can earn $12 per hour if he or she works. There are 30 days per month. Draw the budget constraints that show the monthly consumption-leisure trade-off under the following three welfare programs: a. The government guarantees $600 per month in income and reduces that benefit by $1 for each $1 of labor income. b. The government guarantees $300 per month in income and reduces that benefit by $1 for every $3 of labor income. c. The government guarantees...
An individual can earn $12 per hour if he or she works. There are 30 days...
An individual can earn $12 per hour if he or she works. There are 30 days per month. Draw the budget constraints that show the monthly consumption-leisure trade-off under the following three welfare programs: a. The government guarantees $600 per month in income and reduces that benefit by $1 for each $1 of labor income. b. The government guarantees $300 per month in income and reduces that benefit by $1 for every $3 of labor income. c. The government guarantees...
The average worker at Acme Labs produces 24 widgets per hour, with a standard deviation of...
The average worker at Acme Labs produces 24 widgets per hour, with a standard deviation of 8 widgets. You have invented a new production process, and you hypothesize that your new process will help workers produce more widgets per hour. After implementing the new production process, you take a sample of workers and measure how many widgets they produce per hour. a) What are the null and alternative hypotheses, in symbols? b) (2 points) What are the null and alternative...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT