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PRODUCTION ANALYSIS AND COMPENSATION POLICY / COST ANALYSIS AND ESTIMATION

Marginal Rate of Technical Substitution. The following production table provides estimates of the maximum amounts of output possible with different combinations of two input factors, X and Y. (Assume that these are just illustrative points on a spectrum of continuous input combinations.)

Units of
Y Used

Estimated Output per Day

5
210
305
360
421
470

4
188
272
324
376
421

3
162
234
282
324
360

2
130
188
234
272
305

1
94
130
162
188
210

1
2
3
4
5

Units of X used

A. Do the two inputs exhibit the characteristics of constant, increasing, or decreasing marginal rates of technical substitution? How do you know?

B. Assuming that output sells for $3 per unit, complete the following tables:

X Fixed at 2 Units

Units of
Y Used

Total
Product
of Y

Marginal
Product
of Y

Average
Product
of Y
Marginal
Revenue
Product
of Y

1

2

3

4

5

Y Fixed at 3 Units

Units of
X Used

Total
Product
of X

Marginal
Product
of X

Average
Product
of X
Marginal
Revenue
Product
of X

1

2

3

4

5

C. Assume that the quantity of X is fixed at 2 units. If output sells for $3 and the cost of Y is $120 per day, how many units of Y will be employed?

D. Assume that the company is currently producing 162 units of output per day using 1 unit of X and 3 units of Y. The daily cost per unit of X is $120 and that of Y is also $120. Would you recommend a change in the present input combination? Why or why not?

E. What is the nature of the returns to scale for this production system if the optimal input combination requires that X = Y?

Which of the following combination of inputs is most closely reflective of decreasing marginalrate of technicalsubstitution (MRTS)?
a. oil and natural gas
b. sugar and high fructose corn syrup
c. computers and clerks
d. keyboards and computers
Which of the following is the best example of two inputs that would

Specialty Steel has carefully measured production in its new plant to determine whether it is technically efficient in production. It has found that the production function of the firm is represented by the following equation
Q = 20K^(1/2)L^(1/2)
where Q is output level, K is capital and L is labor.
The firm currently

Please open the word file to view the mathematical notations.
Question
Consider a firm with production function .
(a) Sketch the isoquant diagram of this firm.
(b) Derive the marginalrate of technicalsubstitution between the two inputs. What is the relationship between the marginalrate of technicalsubstitution an

The firm's production function for gadgets, X, depends on the amounts of capital (K), and labor (L) employed:
X = 56K + 8.8L - 2K2 - 0.1L2.
(a) If the firm can sell any output at a price equal to 10, if the wage rate per unit of labor is 8 and the rental per unit of capital is 80, what is the prof

1.
Demand curve: P = 1,000 รข?" 25Q, where P is price and Q is quantity sold per month.
dQ/dP = -1/100
n= (dQ/DP) * (P/Q)
1) Calculate the price elasticity of demand if price equals $250. 2)Calculate the price that maximizes total revenue.
2
Assume that you have $150 that you can spend on either concert tickets o

Consider an economy that uses labor and capital to produce two goods, beer (x) and peanuts (y), subject to technologies that exhibit constant returns to scale. The marginal cost of a 12-ounce can of beer is $0.50. The marginal cost of a 12-ounce tin of peanuts is $1.00. Currently, the economy is producing 1 million 12-ounce cans

A major car company (from Japan), announced a major restructuring plan. to attempt to reverse its 6 percent decline in sales. the company's North American sales were hard hit, where a 29 percent drop in sales. This because of bad loans and financing with banks. In Japan, sales dropped a 56 percent, due to recalls and attempts