Question 1

For price-taking producers, isoprofit curves are always parallel to one another.

Accepted Answer

Isoprofit curves represent the combinations of input factors that result in the same level of profit for the producer, given a fixed output price. Since price-taking producers cannot influence the market price, their isoprofit curves are always parallel because the profit level remains constant regardless of the quantity produced. Any increase in output would result in higher revenue but also higher costs, resulting in the same profit level. Conversely, any decrease in output would reduce revenue and costs, again resulting in the same profit level. Therefore, the isoprofit curves for price-taking producers are always parallel to each other.

Question 2

If the single-input producer choice set is fully convex, the first order conditions of the profit maximization problem are necessary but not sufficient for identifying the profit maximizing production plan.

Accepted Answer

In the context of a single-input producer choice set that is fully convex, the first-order conditions of the profit maximization problem are both necessary and sufficient for identifying the profit-maximizing production plan due to the convexity of the set, which ensures a unique maximum.

Question 3

In the one-input model, the marginal product of labor curve falls below the horizontal axis only if the production frontier slopes down.

Accepted Answer

The marginal product of labor curve falls below the horizontal axis when additional labor decreases total output, which occurs when the production frontier slopes downward.

Question 4

In the one-input model of production, increasing marginal product implies non-convexity of the producer choice set.

Accepted Answer

In the one-input model of production, increasing marginal product means that each additional unit of the input used leads to a greater increase in output than the previous unit. This results in a non-linear relationship between input and output, which leads to non-convexity of the producer choice set. Therefore, the statement is true.

Question 5

An increase in the wage will cause the output supply curve in the one-input model to shift in unless labor is an inferior input.

Accepted Answer

In the one-input model, an increase in the wage would cause the output supply curve to shift left (or decrease) because it would increase the cost of production, not shift in unless labor is considered an inferior input. The concept of inferior or superior inputs is not typically applied to labor in the context of supply curve shifts due to wage changes.

Question 6

A competitive (price-taking) firm will produce so long as its economic profit is sufficiently above zero to enable the firm to pay the owners of the firm for their time and effort.

Accepted Answer

A competitive (price-taking) firm will produce as long as its price is above its average variable cost, even if its economic profit is zero or negative, to cover its variable costs and possibly some of its fixed costs. Economic profit taking into account the opportunity costs, including the time and effort of the owners, does not have to be above zero for production to continue in the short run.

Question 7

In the one-input model, profit is always maximized where marginal revenue product is equal to the input price.

Accepted Answer

The answer of In the one-input model, profit is always...

Question 8

When single-input producer choice sets are non-convex, the first order condition of the profit maximization problem is neither necessary nor sufficient for identifying the profit maximizing production plan.

Accepted Answer

When the producer choice sets are non-convex, the profit maximizing production plan may not even exist or may exist at multiple points. Therefore, the first-order condition alone is not sufficient to identify the profit-maximizing plan. Additional analysis, such as using the second-order condition or examining the boundary points of the choice set, may be necessary.

Question 9

Whenever average cost is increasing, marginal cost must also be increasing.

Accepted Answer

Whenever the average cost is increasing, it could be the case that the marginal cost is decreasing but still positive. For example, if a company produces a certain product and the production level is initially low, the marginal cost might be relatively high due to lower economies of scale. As production increases, the marginal cost might decrease due to increased efficiencies in production, even when the average cost is increasing.

Question 10

In the one-input model, a convex producer choice set implies an upward sloping marginal cost curve.

Accepted Answer

In the one-input model, a convex producer choice set implies diminishing marginal returns to the input. Diminishing marginal returns, in turn, imply an upward sloping marginal cost curve. Therefore, the statement is true.

Question 11

Labor demand curves always slope down.

Accepted Answer

Labor demand curves reflect the inverse relationship between the quantity of labor demanded and the wage rate. As the wage rate increases, employers demand less labor as they seek ways to cut costs. Thus, the demand curve for labor is downward-sloping.

Question 12

Price-taking producers have horizontal marginal revenue curves.

Accepted Answer

Price-taking producers have no market power, so they must accept the market price for their product. This means that their marginal revenue curve is the same as the market price, which is horizontal in a competitive market.

Question 13

If the single-input producer choice set is convex, the marginal product of labor curve must have a negative slope that is getting steeper with increases in labor input.

Accepted Answer

A convex single-input producer choice set implies diminishing marginal returns to labor, which means the marginal product of labor curve slopes downward, but it does not specify that the slope must get steeper with increases in labor input; it only indicates that the marginal product decreases.

Question 14

The law of diminishing marginal product holds so long as the input is not a Giffen good.

Accepted Answer

The law of diminishing marginal product is related to the productivity of inputs in production and is not directly related to the concept of Giffen goods, which pertains to consumer behavior and demand.

Question 15

Output supply curves always slope up in the one-input model.

Accepted Answer

In the one-input model, the output supply curve always slopes upward because an increase in the price of the output will lead to an increase in the quantity supplied of the output, assuming that the input price remains constant.

Question 16

In the one-input model, the marginal cost curve is U-shaped.

Accepted Answer

The answer of In the one-input model, the marginal cost...

Question 17

The output level is constant along any isoprofit line.

Accepted Answer

An isoprofit line represents combinations of output levels of two goods that yield the same profit. The output level of each good can vary along the line as long as the profit remains constant.

Question 18

In the one-input model, a decrease in output price will always cause labor demand to shift in.

Accepted Answer

In the one-input model, where labor is the only input, a decrease in output price reduces the revenue a firm can make per unit of output, which in turn reduces the firm's demand for labor since the value of the marginal product of labor falls.

Question 19

If income effects are sufficiently strong, it may be the case that labor demand curves slope up.

Accepted Answer

Labor demand curves typically slope downward, reflecting that as wages increase, the quantity of labor demanded decreases. The income effect relates to how changes in income affect consumption, not the shape of the labor demand curve, which is primarily influenced by the marginal productivity of labor and wage rates.

Question 20

In the one-input model, the cost curve is the inverse of the production frontier if and only if the input price is 1.

Accepted Answer

In the one-input model, the cost curve is the inverse of the production frontier if and only if the input price is 1. This is because if the input price is 1, the cost of producing a certain level of output is equal to the amount of input used to produce that level of output. Thus, the cost curve will be the same as the inverse of the production frontier. If the input price is not 1, then the cost curve will be scaled up or down depending on the input price, and will not be the inverse of the production frontier.

Quiz 11: One Input and One Output: a Short-Run Producer Model