Note that you need to show your work. There are four questions in total.

  1. Consider the following technological options to make 100 meters of cloth.
Technology option Number of workers Coal required (tonnes)
A 1 6
B 4 2
C 3 7
D 5 5
E 10 1

  1. Plot these points given by technological option on a graph (tonnes of coal in y-axis and number of workers in the x-axis). Label the points, and show what options are irrelevant (you would not pick at any cost).

  2. The price per worker is $20 and price per ton of coal is $10. What technological option is the most efficient one given this cost layout. Show your calculations.

  3. Note that isocost is a curve that shows various combination of technology (coal and workers) with the same exact cost. Write the cost equation in the form \[c=w\times L+p\times R\]. Here, \(c\) is the total cost of your most efficient option from part b, \(w\) is price per worker (per hour), \(L\) is the number of workers, \(p\) is price per ton of coal and \(R\) is tons of coal.

  4. Using the equation in part c., express the equation in the form as \[R=...\].

  5. Plot the line pertaining to part d. on a graph.

  1. This is a follow up question for question 1. Plot the isocost line for Technology B, where this option is described as:
    Technology Number of workers Coal required (tonnes) Total cost ($)
    cost Wage = $10 cost of coal = $20 per ton
    option B 4 2 80

  1. Using a graph, plot the isocost line going through technological option B.

  2. Next, consider a change in cost of inputs such that wage=$10 and cost of coal = $5 per tonne. Technological options A and B can are given as:

Technology Number of workers Coal required (tonnes) Total cost ($)
cost Wage = $10 cost of coal = $5 per ton
optionB B 4 2 50
optionA A 1 6 40

On the graph which you plotted for part a. add isocost curves for option B and option A, after the change in cost of inputs. Show your calculations as to how come up with the isocost lines.

  1. See the following figure:
    Figure 1.

    Figure 1.

  1. From Figure 1, what can we conclude? Pick among four choices that you think are correct. Explain your choice.

\(\underline{choice\;1}\). Technology B is more energy-intensive than technology A.

\(\underline{choice\;2}\). Technology B dominates technology A.

\(\underline{choice\;3}\). Technology A is more energy-intensity than technology B.

\(\underline{choice\;4}\). Technology A is the cost-minimizing technology at all prices of coal and wages.

  1. Looking at the isocost lines in Figure 1, we can conclude that

\(\underline{choice\;1}\). When the wage is $10 and the price of coal is $5, the combination of inputs at point N is more costly than the inputs at point B.

\(\underline{choice\;2}\). Isocosts MN and FG represent the same price ratio (wage/price of coal) but different total costs of production.

\(\underline{choice\;3}\). Isocost HJ represents a higher (wage/price of coal) ratio than isocost FG.

\(\underline{choice\;4}\). Isocost HJ represents all points that can produce 100 metres of cloth at a particular price ratio.

  1. See the relationship between the number of labors and grain:
labor grain
200 20000
400 33000
600 42000
800 50000
1000 57000
1200 63000
1400 68400
1600 73200
1800 77400
2000 81000
2200 84000
2400 86400
2600 88200
2800 89400
3000 90000

  1. Plot the production schedule given by the table above.

  2. Construct a different column along the table to denote the average product of labor.

  3. In a different column calculate the marginal product of labor.

  4. What is the relationship between the average product of labor and marginal product of labor?