## Quiz 6 :

The Theory and Estimation of Production

Answer:

Returns to scale describes what effect on production when all the factor of production are increased. It is a long run phenomena.. There are three types of returns to scale- Increasing return to scale, constant return to scale and diminishing return to scale.

This is to be viewed in a long run phenomenon. All factors of production are variable in the long run. No factor is a fixed factor. Accordingly, scale of production can be changed by changing the quantity of all factors.

Answer:

b. If price of Y decrease then budget line shift upward toward Y-axis. Now with a lower price of Y the producer will be able to purchase more quantity of Y than before with his given budget.

Effect of price decrease in Y

c. If price of X decrease then budget line shift to upward toward X-axis. Now with a lower price of X the producer will be able to purchase more quantity of Y than before with his given budget.

Effect of price decrease in X

d. If Y becomes more expensive and X becomes less expensive then producer will purchase less quantity of Y and more quantity of X. Budget line shift downward on Y axis and shift upward to X axis.

Effect of change in price of Y and X

e. If technology makes the Y input more productive then produces wants to use more quantity of Y. so, budget line shift to upward toward Y axis. Budget line on X axis remains the same.

Effect of increase in productivity in Y

f. If technology increases the productivity of both input by the same proportion then isoquant shifted upward side. Higher isoquant shows the higher production.

Effect of increase in productivity of both by same proportion

Answer:

a.

Let

,

and

denote the wage rate in Mexico, Taiwan and Canada respectively. Let

,

and

denote the marginal product of labor in Mexico, Taiwan and Canada respectively.

Calculate the ratio of marginal product of labor to wage rate for each of the three countries as follows.

Mexico:

Taiwan:

Canada:

For the firm to be optimally allocating its resources, the ratios of the marginal product to wage rate of the three countries should be equal. But that is not the case here, that is, the ratios are different. This implies the firm is not optimally allocating its production resources.

The ratio of marginal product to wage rate (i.e., the units of output yield by the last dollar spent on labor) is highest in Mexico. Therefore, the firm should employ more labor in Mexico.

b.

Suppose for simplicity that the price P of one unit of the firm's output is $1. Suppose the firm manufactures in only one of the three countries - Mexico, Taiwan, and Canada, and the amount of labor employed is L units.

Let

denote the profit of the firm in case the firm manufactures only in Mexico,

denote the profit of the firm in case the firm manufactures only in Taiwan, and

denote the profit of the firm in case the firm manufactures only in Canada.

Scenario 1: The firm manufactures only in Mexico.

Calculate the total cost of the firm by adding the labor cost and the fixed cost.

Calculate the total revenue of the firm by multiplying the price of per unit of output by output produced.

Calculate the profit

by subtracting total cost from total revenue as follows.

Therefore, if the firm bases its manufacturing only in Mexico employing L units of labor, the firm's profit will be equivalent to "

."

Scenario 2: The firm manufactures only in Taiwan.

Calculate the total cost of the firm by adding the labor cost and the fixed cost.

Calculate the total revenue of the firm by multiplying the price of per unit of output by output produced.

Calculate the profit

by subtracting total cost from total revenue as follows.

Therefore, if the firm bases its manufacturing only in Taiwan employing L units of labor, the firm's profit will be equivalent to "

."

Scenario 3: The firm manufactures only in Canada.

Calculate the total cost of the firm by adding the labor cost and the fixed cost.

Calculate the total revenue of the firm by multiplying the price of per unit of output by output produced.

Calculate the profit

by subtracting total cost from total revenue as follows.

Therefore if the firm bases its manufacturing only in Mexico employing L units of labor, the firm's profit will be equivalent to "

."

Observe the following.

In the above inequality, the leftmost expression is

, the middle expression is

and the rightmost expression is

, implying the following.

Therefore, if the firm wants to manufacture only in one location, it should manufacture in Taiwan because there its profit is highest.