Chapter 12

Review Questions

  1. What do economists mean by the term short run?

    2. The short run refers to a period of time over which people cannot fully adjust to a change in conditions. Applied to business decisions, it refers to a period over which a firm cannot change the quantity of some input.

    As an example, think about an owner of a small store that sells (himself) cameras. There are lots of inputs that he uses in the process of providing (producing) service to customers: for example, the cameras, his labor, electricity, rental space. In this situation how long is short run depends on which factor he wants to change. As far as electricity is concerned there does not seem to be a problem of getting more of that input regardless of the time span: electricity is an variable input for any time span. On the other hand, he is not able to get more cameras in seconds. If his supplier has a depot in the same time, he can get them in a couple of hours, so the short run corresponds to time spans shorter than that. If he needs to order the cameras for delivery, the short run increases do a couple of days.

    Finally, if he wants to change the size of his store (either by moving or by building an extra part), the short run may correspond to weeks.
     
     

  2. What are fixed inputs? Variable inputs? Give examples of each.

    3. Fixed inputs are inputs whose quantities a firm cannot change in the short run. On the other hand, variable inputs are such inputs, whose quantities a firm can change in the short run.

    In the example in question 1, in a time span of a few days electricity and cameras are variable inputs and the rental space is a fixed input.
     
     

  3. What are fixed costs? Variable costs?

    4. Fixed costs are costs of fixed inputs. Variable costs are costs of variable inputs. Using again the example from question 1, the costs of electricity is a variable cost and the rent is a fixed cost.

    As far as the cameras are concerned, the cost of having a stock of them in the store corresponds to the opportunity cost of money invested in them (he could instead put some of the money into stocks and earn interest). Another cost is the opportunity cost of the space: the more cameras he has in the store, the more crowded it gets (and, for example, it's more difficult to find something in the stock or more difficult to keep the place in order).
     
     

  4. Under what conditions does a firm shut down in the short run? Under what conditions does it produce at a loss? Explain.

    In the short run the firm shuts down when the smallest losses it can suffer while producing are higher than the losses it incurs by shutting down.

    The losses when firm produces are equal to the difference between total costs and total revenue. The total costs consist of the fixed costs and total variable costs.

    The losses when the firm shuts down are equal to the fixed costs.

    So if there is no level of output such that the total variable costs are smaller than total revenue, the firm is better off by shutting down.

    The same reasoning leads to the following statement: It is optimal for a firm to produce at a loss in the short run if:

 

5. Change the numbers in Table 1 so that fixed cost is $15 instead of $10. Does this change affect other numbers in the table? Which ones? Explain how this change affects the firm's short-run decisions and profit.

    Quantity
    (Q)    		 Price
    (P)    		 Total Revenue
    (TR)    		 Marginal Revenue
    (MR)    		 Total Cost
    (TC)    		 Total Variable Cost
    (TVC)    		 Marginal Cost
    (MC)    		 Profit
    1 16 16 16 43 28 28 -27
    2 15 30 14 57 42 14 -27
    3 14 42 12 59 44 2 -17
    4 13 52 10 61 46 2 -9
    5 12 60 8 63 48 2 -3
    6 11 66 6 66 51 3 0
    7 10 70 4 70 55 4 0
    8 9 72 2 75 60 5 -3
    9 8 72 0 81 66 6 -9
    10 7 70 -2 88 73 7 -18
    11 6 66 -4 96 81 8 -30
    12 5 60 -6 105 90 9 -45

    The numbers in the table that have changed are highlighted in the new table: despite the total cost only the column with profits has changed. The optimal decision of the firm does not change: the marginal cost and marginal benefits are unchanged, which implies that the optimal choice of output stays the same. Also, at that optimal quantity, the total revenue and total variable cost do not change, so the firm does not have incentives to change its decision about producing or shutting down.

    The profits go down by the amount of the increase of the fixed costs: they drop from $5 to $0.
     
     
     

6. What are the definitions of average total cost, average fixed cost, and average variable cost?

    Average total cost (ATC) is the overall per-unit cost (total cost divided by the quantity produced).

    Average fixed cost (AFC) is total fixed cost divided by the quantity produced.

    Average variable cost (AVC) is total variable cost divided by the quantity produced.
     
     

7. What is capacity output?

Capacity output is the level of output that minimizes average total cost.

 

8. Explain the connection between short-run and long-run average total cost curves.

    A short-run average cost curve lies above the long-run average cost curve. There are in fact many short-run average total cost curves (SRAC curves) and only one long-run curve (LRAC). The particular SRAC corresponds to a given amount of the fixed input. The LRAC touches the SRAC curves from below.

    The reason is the following. It is always possible to produce given amount of output as cheap in the long-run as in the short-run: simply employ the same amount the same amount of all inputs. Hence the LRAC can never be above SRAC.

Furthermore, in the long run the firm can choose a different amount of the fixed input to decrease the average cost. Hence for most quantities the LRAC is below a particular SRAC.

 

9. How are short-run supply curves related to costs?

    A firm's short-run supply curve is the portion of its marginal cost curve lying on or above the average variable cost curve.

     

10. How are producer surplus and profit related in the short run?

    In the short run, the producer surplus is equal to profits plus (unavoidable) fixed costs.
     
     

11. What is the capacity output of the firm profiled in Table 2?

It is 11: at that quantity the average total cost is minimized.
 
 

12. What is the marginal product of an input? What is the value of an input's marginal product?

    The marginal product of an input is the increase in a firm's total output when it adds a little more of this input while keeping quantities of other inputs fixed.

    The value of an input's marginal product is the marginal product multiplied by price of the output. In other words, it is by how much the total revenue increases when we increase the amount of this input by a unit (keeping the amount of other inputs fixed).
     
     

13. Explain the law of diminishing returns.

    The law of diminishing returns is the principle that raising the quantity of an input eventually reduces its marginal product, given that the quantity of some other input remains fixed. For an example see page 287.
     
     

14. Why does the short-run marginal cost curve slope upward? Why does a firm's short-run supply curve slope upward?

    The short-run marginal cost curve slopes upward because of the law of diminishing returns.

    In the short-run the amount of the fixed inputs remains constant, no matter what is the level of production.

    So suppose that we start with some quantity of production at which the marginal product of the variable input is 0.5. Then, in order to increase the output by a unit, the firm has to employ two more units of the variable input and the marginal cost is equal to 2 times the price of the variable input.

    By the law of diminishing returns, at the higher quantity the marginal product of the variable input is lower. In order to increase the output by another unit the firm needs to employ more than 2 units of the variable input.

    Hence the marginal cost of the additional unit of production is higher than of the last one.

    This reasoning is true for any output level (for which the law of diminishing returns holds): the more the firm wants to produce, the higher is the marginal cost.

    The short-run supply curve slopes upwards as it is equal to the marginal cost curve.
     
     

15. What determines a firm's demand for an input? How does your answer relate to the general rule for rational choice?

    The firm's demand for an input at a given price of it depends on the value of the marginal product of this input. The firm chooses such a quantity of the input at which the price of it is equal to the value of the marginal product.

    This is another application of the general rule for rational choice. For the firm the marginal benefit from employing another unit of an input is equal to how much this extra unit increases the total revenue: the value of the marginal product. The marginal cost of the input is equal to its price. Hence the rule of rational choice states that if the value of marginal product is higher than the price of the factor, the firm should buy more of it. When it is smaller, the firm should by less of it. Finally, when they are equal, the firm is employing the optimal amount of that factor.
     
     

16. How would the numbers in the last column of Table 3 (which show the value of the marginal product of labor) change if the product price were $2.00 each instead of $0.50 each?

    They would be four times larger.
     
     

17. Suppose that the firm in Table 3 hires six workers who earn $30,000 per year. What is its marginal cost of producing containers?

    When there are 5 workers employed the total output is 270,000 and with six workers it is 300,000. So employing an extra worker gives an increase of 30,000 units of output. The extra cost of these extra units is the annual salary of the sixth worker: $30,000. So the additional cost per one extra unit is $1. This is the marginal cost.
     
     

18. What is a discounted present value?

    The discounted present value of a future amount of money is the money you would need to save and invest now to end up with that specific amount of money in the future.

    In other words, it is the value today (at the present time) of receiving that money in the future.
     
     

19. What is the value of a firm?

    The value of a firm is the discounted present value of its expected future profits.
     
     

20. Explain in words why $100 today is worth more than $100 to be received in the future, even if the prices do not change.

    It is better to receive money today than in the future because you can save money that you have today and earn interest. For instance, if you have $100 today and the interest rate is 4 percent per year, you can turn your money into $104 next year.
     
     

21. What is the general formula for the discounted present value of X dollars paid every year forever?

    The formula is:

    ,

    where i denotes the interest rate.
     
     

22. What is the general formula for the discounted present value of X1 dollars to be paid 1 year from now, and X2 dollars to be paid 2 years from now, X3 dollars to be paid 3 years from now, and so on?

    The formula is:

    where i denotes the interest rate.
     
     

23. Perform the following calculations.

  1. If the interest rate is 10% per year, what is the discounted present value of $200 to be paid 1 year from now? What if the interest rate is 5%?
  2. Suppose that the interest rate is 10% per year. Find the discounted present value of $20,000 to be paid 2 years from now.
  3. Suppose that the interest rate is 10% per year. What is the discounted present value of $10,000 to be paid 1 year from now plus $10,000 to be paid 2 years from now?
a) At 10% per year, the discounted present value of $200 to be paid 1 year from now is:
At 5%, the discounted present value of $200 to be paid 1 year from now is:


b. The discounted present value of $20,000 to be paid 2 years from now at 10 percent interest is:

 

  1. The discounted present value of $10,000 1 year from now and 2 years from now when the interest rate is 10% is:


24. If people expect a firm to earn profits of $100,000 per year, every year, forever, and the interest rate is 5% per year, what is the value of the firm?

    The value of the firm is:



25. Explain the statement: "Fixed costs are unavoidable in the short run."

    Fixed costs correspond to payments for such inputs that the firm is not able to change quantity of in the short-run. It has to pay for these inputs no matter what. So they are unavoidable in the short-run.
     
     

26. Discuss the statement: "A rational firm might decide to produce in the short run but shut down in the long run, even if the demand for its product and its costs do not change."

    Fixed costs are the reason behind a rational firm's decision to produce in the short run, but shut down in the long run, even if demand for its product and its costs do not change.

    When the fixed costs are high, the optimal decision of the firm in short-run can be to produce and incur losses.

    In the long run, when the firm can change all the inputs so there are no fixed costs. The firm can always exit and have zero profits. It will do so if there is no combination of all the inputs that allows for profitable production.
     
     

27. Comment on this statement: "A good businessperson never sells a product for less than the cost of producing it."

    In the short run when certain costs are fixed, there may be instances where the firm produces at a loss because its loss would be even larger if it were to shut down. In this case, the business would be selling its product for less than the cost of producing it, however, the losses would be lower than if it shut down operations altogether.

    Notice that in this case the cost of producing the good is measured by the Average Total Cost. The firm would never sell for a price below Average Variable Cost or below the Marginal Cost.
     
     

28. Suppose that the firm in Table 1 has a fixed cost of $20 instead of $10. How does this change affect other numbers in the table? How does it affect the firm's short-run decisions and profit?

    The new table is:
     
    Quantity

    (Q)

    		Price

    (P)

    		Total Revenue

    (TR)

    		Marginal Revenue

    (MR)

    		Total Cost

    (TC)

    		Total Variable Cost

    (TVC)

    		Marginal Cost

    (MC)

    		Profit
    1 16 16 16 48 28 28 -32
    2 15 30 14 62 42 14 -32
    3 14 42 12 64 44 2 -22
    4 13 52 10 66 46 2 -14
    5 12 60 8 68 48 2 -8
    6 11 66 6 71 51 3 -5
    7 10 70 4 75 55 4 -5
    8 9 72 2 80 60 5 -8
    9 8 72 0 86 66 6 -14
    10 7 70 -2 93 73 7 -23
    11 6 66 -4 96 81 8 -35
    12 5 60 -6 110 90 9 -50

    The changed numbers have been highlighted. Increase of the fixed costs does not affect firm's decisions (see explanation in question 5). The profits go down by the amount of increase of the fixed cost: from a profit of $5 to a loss of $5.
     
     

29. Change the numbers in Table 1 on page 279 to make the firm a price taker by assuming that the price is 8 for every quantity (so that every number in the Price column is 8). Notice that marginal revenue also becomes 8 for every quantity. How does this change affect the firm's short run decisions and profit?

    The new table is:
     
    Quantity

    (Q)

    		Price

    (P)

    		Total Revenue
    (TR)    		 Marginal Revenue
    (MR)    		 Total Cost
    (TC)    		 Total Variable Cost
    (TVC)    		 Marginal Cost

    (MC)

    		Profit
    1
    8
    8
    8
    38
    28
    28
    -30
    2
    8
    16
    8
    52
    42
    14
    -36
    3
    8
    24
    8
    54
    44
    2
    -30
    4
    8
    32
    8
    56
    46
    2
    -24
    5
    8
    40
    8
    58
    48
    2
    -18
    6
    8
    48
    8
    61
    51
    3
    -13
    7
    8
    56
    8
    65
    55
    4
    -9
    8
    8
    64
    8
    70
    60
    5
    -6
    9
    8
    72
    8
    76
    66
    6
    -4
    10
    8
    80
    8
    83
    73
    7
    -3
    11
    8
    88
    8
    86
    81
    8
    2
    12
    8
    96
    8
    100
    90
    9
    -4

    Now the optimal decision is to produce 11 units - for that quantity the marginal cost is equal to marginal revenue. The profits are $2.
     
     

30. How does an increase in a firm's fixed cost affect:

  1. Its profit-maximizing short-run level of output?
  2. Its short-run profit?
  3. Its decision to stay in business or shut down in the short run?
a) An increase in a firm's fixed cost has no effect on the profit-maximizing short-run level of output.

b) The short-run profit decreases by the same amount that the fixed cost increases.

c) In the short-run it has no effect on the decision to produce or to shut down.
 
 

31. How is the short-run supply curve of a price-taking firm related to its cost of production? Explain the connection in as much detail as you can.

The short-run supply curve a price-taking firm is the part of its marginal cost curve that lies above its average variable cost curve.

If the firm is a price taker, the marginal revenue is equal to price.

First, notice that the MC curve crosses the AVC in minimum (be sure you can explain why).

Second, when the marginal revenue is smaller than minimum of AVC, the firm is better off shutting down than producing any level of output (be sure you can explain this statement too).

These two observations explain why only the art of MC that lies above AVC corresponds to the supply of the firm.

Now, we explain why the supply curve corresponds EXACTLY to this part of the MC curve.

Suppose that the price is p and that it is higher then minimum of AVC, so that we know that the firm is better off producing than shutting down. There are three possibilities: the firm can:

  1. choose such a level of output that the MC is higher than p,
  2. choose such a level of output that the MC is equal to p,
  3. choose such a level of output that the MC is smaller than p,
We explain why the first and last alternatives are not optimal:
  1. If the firm plans to produce such quantity at which MC is higher than the price, then the last unit produced costs the firm more than the price. By not producing it the firm avoids this loss. So it can be never optimal for a firm to produce so high output that the MC is higher than the price.
  1. If the firm plans to produce such quantity at which MC is lower than the price, then producing an extra unit is cheaper than the price the firms can get for it. So by increasing production the firm can earn an extra profit. So it cannot be optimal to plan to produce such a low output.
So we are left only with possibility b): the optimal decision of the firm is to choose such a level of output that equalizes the MC and the price. Therefore the short-run MC curve represents the short-run supply curve.