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

Question 1

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

Answer 1

True

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.

Answer 2

False

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.

Answer 3

True

Question 4

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

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.

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.

Question 7

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

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.

Question 9

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

Question 10

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

Question 11

Labor demand curves always slope down.

Question 12

Price-taking producers have horizontal marginal revenue curves.

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.

Question 14

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

Question 15

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

Question 16

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

Question 17

The output level is constant along any isoprofit line.

Question 18

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

Question 19

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

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.

Question 21

Calvin buys newspapers and delivers them (by bike) to his customers' houses while Hobbes sells lemonade at his lemonade stand.One day they compare notes and find that Calvin, after paying for the newspapers and the maintenance on his bike, clears $5 per hour while Hobbes, after paying for the lemonade ingredients and upkeep of his lemonade stand, clears $4.50 per hour.The newspaper and lemonade businesses are the only possible trades for Calvin and Hobbes.
a.If Calvin and Hobbes are identical, how much economic profit (per hour) is each making?
b.Suppose Hobbes is slower on his bike than Calvin -- and he could only deliver half as many newspapers per hour.What's his economic profit in the lemonade business?

Question 22

With all other inputs held fixed, the marginal product of any input must eventually increase as more of that input is hired.

Question 23

Every profit-maximizing producer is cost minimizing.

Question 24

Which of the following may be consistent with profit-maximizing behavior by a price-taking producer:

A)Output is set where price is equal to marginal cost.
B)Output is set where marginal revenue is equal to marginal cost.
C)No output is produced.
D)(a) and (b)
E)(a) and C
F)(b) and (c)
G)All of the above
H)None of the above

Question 25

If profit from producing would be negative, producers will shut down.

Question 26

Suppose you solve the profit maximization problem for a single-input, price-taking producer whose technology is given by The labor demand function is
a.Suppose Might in fact be the correct labor demand function? Explain.
b.Suppose Might in fact be the correct labor demand function? Explain.
c.Intuitively explain how (b) might arise from the profit maximization problem.

Question 27

Every cost-minimizing producer is profit-maximizing.

Question 28

Suppose a price-taking firm uses a single input - labor - to produce an output x.The production technology has diminishing marginal product of labor throughout.
a.On a graph with labor hours on the horizontal and output on the vertical axis, illustrate the production frontier for this firm.
b.For a given wage rate w and output price p, illustrate three isoprofit curves corresponding to profit levels π < π'< π" -- indicating slopes and intercepts.Suppose the profit maximizing plan results in profit π'.Then use isoprofit to illustrate the profit maximizing production plan for the firm and show how w and p are related to the marginal product of labor at that plan.
c.Where on your graph do all cost-minimizing production plans lie?
d.On a graph with output on the horizontal and dollars on the vertical axis, illustrate the shape of the cost curve for the firm (holding fixed w).Then suppose that, in addition to labor costs, the firm has to pay a recurring (long run) fixed cost F.Where does the long run cost curve lie in relation to the initial (short run) cost curve you drew?
e.On a separate graph, illustrate the short run marginal and average cost curves.Then, on the same graph illustrate the long run marginal and average cost curves in the presence of the recurring fixed cost.f.Indicate where in your graph you can locate the short and long run supply curves for this firm.

Question 29

Price taking producers make zero economic profit when price falls

A)at the lowest point of the average cost curve
B)at the point where marginal cost crosses average cost
C)at the lowest point of the marginal cost curve
D)both (a) and (b)
E)both (a) and C
F)both (b) and (c)
G)All of the above
H)None of the above

Question 30

Suppose a single-input production function has initially increasing but eventually decreasing marginal product -- and suppose we know that an interior solution is profit maximizing.In this case, the first order condition for the profit maximization problem

A)is necessary for identifying the profit maximizing production plan.
B)is sufficient for identifying the profit maximizing production plan.
C)is both necessary and sufficient for identifying the profit maximizing production plan.
D)is neither necessary nor sufficient for identifying the profit maximizing production plan.

Question 31

Since the marginal product of labor can increase initially as I hire more workers, demand for labor is also upward sloping for the initial workers I hire.

Question 32

Suppose a single-input production function has initially increasing but eventually decreasing marginal product.In this case, the first order condition for the profit maximization problem

A)is necessary for identifying the profit maximizing production plan.
B)is sufficient for identifying the profit maximizing production plan.
C)is both necessary and sufficient for identifying the profit maximizing production plan.
D)is neither necessary nor sufficient for identifying the profit maximizing production plan.

Question 33

Suppose a technology is described by the production function
a.For a price taking producer who faces output price p and wage w, derive the first order condition and interpret it.
b.Without knowing more about the function f, is the condition you derived in (a) either necessary or sufficient for deriving the profit maximizing production plan? Explain.
c.Suppose .Derive the first order condition you illustrated in (a) and solve for .
d.For what values of is this first order condition necessary and sufficient for deriving a profit maximizing production plan? Explain.

Question 34

Labor demand curves are homogeneous of degree zero.