1) Economic Profit is Total Revenue minus Total Cost, where Total Cost includes both Accounting Cost and Opportunity Cost.  The key point is that Economic Profit considers Opportunity Cost, something that is often neglected when calculating profit.

2) When studying a profit-maximizing firm in a perfectly competitive industry in the short run, technology, output price, input prices and at least one input are held constant as parameters.  Why?  The prices are held constant because the firm is in a perfectly competitive industry.  Technology and at least one input are held constant because the firm is in the short run.  (If the firm were in the long run, then it would be able to choose a different technology and different levels for all of its inputs.)

3) A Production Function is a description of a firm's technology.  A production function gives the maximum amount of output that can be produced from various combinations of inputs, given a fixed production technology.  Note: we graph a production function indirectly by graphing the Isoquants that come from it.

4) Economists measure the productivity of an input by calculating the input's Total Product, Average Product and Marginal Product.  Each input has a Total Product, an Average Product and a Marginal Product.

5) The completed table is shown below.  It is important to notice that TP_L , AP_L and MP_L are different at each level of L. Remember that the Cost-Minimizing Rule depends on MP_L.  If a firm bases its cost-minimizing decisions on TP_L or AP_L, it will be led astray, because TP_L and AP_L are different from MP_L.

6) The "Law of Diminishing Marginal Product," also known as the "Law of Diminishing Returns," is simply the commonly observed pattern that as a firm uses more and more of a particular input, holding the use of all other inputs constant, then the marginal product ("MP") of the input will begin to decrease.  For example, notice in the table in the problem above that as L increases, MP_L decreases.  Although this pattern doesn't hold for all production processes, it holds so often that it is often used as a beginning assumption when conducting an analysis.

7) a. Recall that at each endpoint of an isocost line, it is true that: Units of Input = (Total Cost)/(Price of Input).  Hence, at point A on isocost line AB, it is true that: 60 = (Total Cost)/($20).  Thus, Total Cost is 60*$20 = $1200,    b. Use the formula Units of Input = (Total Cost)/(Price of Input) at point C to find Total Cost, then use the formula again at point D (plugging in the Total Cost you found at point C) to find that the price of labor is $20,   c. From the formula Units of Input = (Total Cost)/(Price of Input), we know that if point D shifts out to point E, then either Total Cost increased or the price of labor decreased.  However, because point C does not change, we know that the Total Cost did not change.  Hence, it must be that the price of labor decreased.   d. -(price of labor / price of capital)

8) a. Use the formula Units of Input = (Total Cost)/(Price of Input) at either endpoint of the isocost line to find that Total Cost = $2000,  b. slope = rise/run = -100/200 = -1/2,  c. At point C, the slope of the isoquant is equal to the slope of the isocost, namely -1/2,  d. Point C, because point C is on an isoquant that produces a higher level of q, yet point C remains on the same isocost as point B and thus has the same total cost.

9) Recall that the slope of an isocost is -P_L/P_K. If P_K increases, the slope becomes less negative, so the isocost lines in the figure will become less steep, or flatter. If the isocosts become flatter, then the new point of tangency with the given isoquant will be at a point like point B. Hence, if P_K increases, the firm will use less K and more L to produce the target level of Q. If P_L increases, the slope -P_L/P_K become more negative, which means the isocost lines become steeper. With steeper isocosts, the tangency with the given isoquant will occur at a point like point C--the firm will use more K and less L in its production of the target level of Q.

10) Recall the Cost-Minimizing Rule: MP_L/P_L = MP_K/P_K.  If we plug in the given information, we find that MP_L/P_L = 5/2 = 2.5, whereas MP_K/P_K = 10/5 = 2. Hence, the firm is NOT following the Cost-Minimization Rule.  In order to follow the rule, the firm should purchase more labor and less capital.  The reason why hinges on the Law of Diminishing Marginal Product.  If the firm uses more labor, MP_L will decrease, due to the Law of Diminishing Marginal Product.  At the same time, if the firm uses less capital, MP_K will increase, due to the Law of Diminishing Marginal Product operating "in reverse."  If MP_L decreases and MP_K increases, then the firm will move closer to MP_L/P_L being equal to MP_K/P_K, which is the Cost-Minimization Rule.

11) Recall that the slope of an isoquant is equal to -MP_L/MP_K and the slope of an isocost is equal to -P_L/P_K.  At point A, the slope of the isoquant is more negative than the slope of the isocost, hence -MP_L/MP_K < -P_L/P_K.  Canceling out the negative (which flips the direction of the inequality symbol), MP_L/MP_K > P_L/P_K.  Now, cross multiply to get MP_L/P_L > MP_K/P_K.  This last result tells us that the firm is not minimizing costs, because if it were, we would have found MP_L/P_L = MP_K/P_K.  I would suggest to management that they hire more labor, which would decrease MP_L, and less capital, which would increase MP_K, moving the firm closer to the Cost-Minimization Rule of MP_L/P_L = MP_K/P_K.  On the other hand, if the firm were operating at point B, the slope of the isoquant is less negative than the slope of the isocost, hence -MP_L/MP_K > -P_L/P_K.  At point B, an analysis similar to that used for point A would suggest that the firm should hire less labor and more capital.

12a) 9 units of L

12b) 20 units of K

12c) At each endpoint of each isocost line, it is true that: Units of Input = (Total Cost)/(Price of Input).   Rearranging this equation to solve for TC, at each endpoint of each isocost line along the L axis it is true that: TC = L·P_L.  Consider the isocost line that is tangent to the Q = 100 isoquant.  At its endpoint on the L axis, TC = L·P_L = 10·$40 = $400.

12d) Calculate the TC of producing each level of Q.  Recall that at the endpoint of each isocost line along the L axis, TC = L·P_L.  In the table below, this fact is used to calculate the TC of producing each level of Q.  If the firm's budget is $600 in Total Cost, then the firm can produce up to 200 units of Q.

12e) Based on the data in the table above, we can construct the following Short Run Total Cost Curve graph:

13)  a. TFC is the vertical distance between TC and TVC (that is, TFC = TC-TVC).  When the number of Microwave Ovens produced is zero, then TFC = $500-$0 = $500.  Similarly, when 3 ovens are produced, TFC = $1000-$500 = $500, or when 6 ovens are produced, TFC = $1200-$700 = $500.  We find that TFC = $500 regardless of the number of ovens produced because fixed costs remained just that, fixed, regardless of the level of production.  b. Recall that AVC = TVC/Q, so AVC = 500/3 = $166.7,  c. Recall that MC = TC / Q. So, when producing the third oven (that is, when moving from unit 2 to unit 3 along the oven axis) we find that MC = (1000-850)/(3-2) = $150.

14a) 

14b)  Refer to the figure below.  When MC is below ATC, ATC is decreasing.  Likewise, when MC is below AVC, AVC is decreasing. When MC is above ATC, ATC is increasing.  Similarly, when MC is above AVC, AVC is increasing.

14c) Following the Profit-Maximizing Rule, produce the level of Q where MR=MC (when there is more than one MC that matches MR, then choose the MC where MC's are increasing, not decreasing).  In this case, MR = $30, so we need to find where MC = $30.  MC = $30 in two places in the table above.  We want to choose the second MC from the top of the table (that is, the MC where the MC's are increasing).  At this MC, we find that Q = 7.  So, the firm should produce Q = 7 in the short-run.   Recall that TR = P_Q*Q, so TR =  $30*7 = $210.  Recall that Econ. Profits = TR - TC, so Econ. Profits = $210 - $240 = -$30 (a loss of $30)  (Note: We know that TC is $240 by looking in the row corresponding to Q = 7 in the table above.)

14d) Using methods similar to those used in the preceding problem, we find that the firm should produce Q = 9.  Similarly, TR = $50*9 = $450.  Econ. Profits = TR - TC = $450 - $330 = $120

14e) Zero units of Q!!!  The price of $10 is below minimum AVC of $17--the shut-down price!  The firm earns zero total revenue, but it must still pay TFC, so Economic Profit = Total Revenue of zero - Total Fixed Cost = -$100 (a loss of $100).

15a)

Q     L     TFC     TVC         TC          AFC         AVC     ATC     MC
0     0       $200     $0           $200        -----        -----     -----     -----
1     10     $200     $500       $700        $200       $500     $700     $500
2     15     $200     $750       $950        $100       $375     $475     $250
3     18     $200     $900       $1,100     $67         $300     $367     $150
4     22     $200     $1,100    $1,300     $50         $275     $325     $200
5     28     $200     $1,400    $1,600     $40         $280     $320     $300
6     36     $200     $1,800    $2,000     $33         $300     $333     $400
7     48     $200     $2,400    $2,600     $29         $343     $372     $600

15b) Break-Even Price = minimum ATC = $320.  Shut-Down Price = minimum AVC = $275.

15c) Following the Profit-Maximizing Rule: the firm should produce the level of Q where (1) MR = MC and (2) where MC is rising.  Recall that MR always equals P_Q for a firm in a perfectly competitive market. Given that MR = P_Q = $400, find where MC = $400 in the table above, and then read the corresponding Q from the first column in the table.  The firm should produce 6 units of Q. (Notice that MC is also equal to $400 somewhere between 1 and 2 units of Q.  However, at this level of Q, MC is still falling, so we don't want to halt production at this level of Q.  Rather, we want to increase Q until MC is rising and MC = $400.  This occurs at 6 units of Q.)

15d) Economic Profit = Total Revenue - Total Cost  =  (P_Q*Q) - (TC) = ($400*6) - $2,000 = $2400 - $2000 = $400.

Multiple Choice

1c, 2a, 3a, 4c, 5b, 6c, 7a, 8c, 9b, 10a, 11c, 12d, 13b, 14a, 15d, 16c, 17a, 18b, 19a, 20c, 21b, 22b, 23a, 24c, 25a, 26b, 27d, 28c, 29b, 30c, 31b, 32c, 33d, 34c, 35b, 36c, 37c, 38c, 39c, 40a