Problem Set 4 (Practice for Exam 1)

You are in process of preparing for your upcoming exam. The production process between hours spent studying (input) and your exam score can be mapped by the following empirical production process.

Table 1.

In a separate column, calculate the average product per hour you spend studying.
In another column, calculate the marginal product per additional hour you spend studying.
Plot the empirical production function as given by Figure 1, the average and marginal product per hour spent studying on a graph.
What can you say about the relationship between the marginal and average product per hour spent studying. Why is the relationship as it is?

The following figure plots the empirical production function as presented in Table 1, along with tangential lines at points A and B.

Figure 1.

Using Table 1 and Figure 1 estimate the slope of the tangential line running across point A.
Estimate the slope of the tangential line of point B.
Using you answers from part a and b, what can you say about the number of hours spent studying and diminishing marginal product of labor?

Consider that you care about both your score and your leisure time. It is obvious from Table 1 that there is a trade-off between hours spent studying and time you have left for leisure. Say your preference set between exam score and leisure is as follows:

	A’	B’	C’	D’	E’	F’	G’	H’	I’
Final Score	79.5	80	81	81.8	83	85.5	88.5	91.5	94.5
Free Time	20.0	18	16	15.0	14	13.0	12.0	11.0	10.0

Table 2.

Note that you are indifferent between any of these points – each point gives you the same level of happiness.

Express your preference set in Figure 2 by using an indifference curve.
Calculate the marginal rate of substitution when you move from preference A’ to B’ vs. when you move from H’ to I’.

Table 3.

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).
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.
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.
Using the equation in part c., express the equation in the form as \[R=...\].
Plot the line pertaining to part d. on a graph.

Table 4.

Plot the production schedule given by the table above.
Construct a different column along the table to denote the average product of labor.
In a different column calculate the marginal product of labor.
What is the relationship between the average product of labor and marginal product of labor?

name	Production if 100% of time is spent on one good
Greta	1,250 apples or 50 tonnes of wheat
Carlos	1,000 apples or 20 tonnes of wheat

Table 5.

Draw the production possibility frontier (ppf) for Greta and Carlos. Note that ppf shows the combination of apples and wheat Greta can produce (same with Carlos).
Is the slope of the ppf constant?
Who has the absolute advantage in both crops? Show work. Explain.
Who has the comparative advantage in growing apples? Show work. Explain.
Who has the comparative advantage in growing wheat? Show work. Explain.
What are some drawbacks of specialization?