McPeak                                                           Name:_______KEY__________________

PAI 723

Exam 2

All numbered questions are worth 2 points each, sub questions worth an equal share of these 2 points.

1) Complete the following table.

 Output Fixed Cost Total Cost Average Cost Marginal Cost Variable Cost 0 12 12 NA NA NA 1 12 23 23 11 11 2 12 33 16.5 10 21 3 12 45 15 12 33 4 12 58 14.5 13 46 5 12 72 14.4 14 60 6 12 87 14.5 15 75

a)  Is this a short run or long run information on cost?  Why?

Short run since fixed costs are greater than zero.  There are no fixed costs / fixed inputs in the long run.

b)      If the price of the good produced is currently 14, what level of output meets the profit maximizing condition?

Step one:  where is MR=MC?  Where is P=MC?  Where is 14=MC.  Output of 5.

Step two:  Am I better producing at 5 or zero.  If 5, profit is 5*14-72, or 70-72, or -2.  If I produce zero output, I earn -12.  Better at output of 5.  [Alternatively, at output of five, AVC=12, P=14>AVC.

c)      Draw the fixed cost, the variable cost, the average cost, and the marginal cost curves based on the information in this table.

2) You know that the demand curve is defined by the following function:  P=60-3*Q.

a.       Use the bisection rule to define the marginal revenue curve

MR=60-6*q

b.      If total cost is defined by 6*Q, then you know MC is 6 for all possible levels of Q.  Is average cost different from marginal cost in this setting?  Why or why not?

NO it is not different, AC=MC if this is the case.

WHY?  if TC=6*Q, then AC=(TC/Q)=(6*Q/Q)=6.  MC=AC=6.

c.       At what Q do marginal cost and marginal revenue cross?

60-6*q=6, so 54=6*q, q=9.

d.      What is the implied selling price at this Q?

P=60-3*q, and if q=9, then 60-3(9)=33

e.       Is the firm better off setting Q=0 and shutting down or producing at the Q you noted in (c)?  Explain your reasoning briefly

Profit if I produce at the (33, 9) pair is Profit=33*9-6(9)=243. I produce zero, I get zero.  I would choose 243 over zero in profit, so not better off shutting down.  Alternatively, from (b), I know AC=6, from (d) I know AR = 33, so I earn a profit per unit of 27, so that beats earning zero profit per unit on average!
Assume the market for this commodity was to become a perfectly competitive market for some reason.

a.       What are the market price and amount of quantity in the market if all firms in the competitive market had identical cost structures to the monopoly firm (MC=6) and the demand curve was unchanged?

60-3*q=6, so 54=3*q, q=18.  Market price is 60-3*18, or 6.

b.      Show the competitive case in comparison to the monopoly case on a single graph.

Note on this the equilibrim points:  pstar, qstar, pmonopoly, qmonopoly

c.       Calculate the area in numbers of consumer surplus, producer surplus, and total social welfare under the competitive and the monopoly structure.

 Competitive Market Structure Monopoly Market Structure Consumer Surplus =(1/2)*(60-6)*18=486 =(1/2)*(60-33)*9=121.5 Producer Surplus 0 =(33-6)*9=243 Total Social Welfare 486 364.5

4) Circle the correct answer for each.

a)      In a perfectly competitive market the area corresponding to producer surplus is the area:

1.      Below the demand curve and above the price line to the left of the optimal quantity.

2.      Above the demand curve and below the supply curve to the right of the optimal quantity.

3.      Above the supply curve and below the price line to the left of the optimal quantity.

4.      Below the supply curve and above the x –axis to the right of the optimal quantity.

b)      Neutral Technological Progress:

1.      Increases the marginal rate of technical substitution for the isoquant.

2.      Decreases the marginal rate of transformation for the isocost.

3.      Leaves marginal rate of technical substitution for the isoquant unchanged.

4.      Increases the cost of producing a given level of output with a given input bundle.

c)      Economic Cost:

1.      Captures both current and historical costs.

2.      Includes both explicit and implicit costs.

3.      Is equal to fixed cost in the case of a monopoly.

4.      Is downward sloping when average product is greater than zero.

d)     The long run supply curve for the individual firm in a perfectly competitive market is:

1.      The average fixed cost curve at and above the average cost curve, q=0 elsewhere.

2.      The inverse of the industry supply curve.

3.      The marginal cost curve at and above the point where AC(Q)=MC(q), q=0 elsewhere.

4.      Derived from the price consumption curve as the market price varies for that good.

5) Assume the rental rate of capital is 10 and the wage rate is 20.

a.       Draw an isocost curve for a total cost level of 120.

Rather than draw it, let me describe it and leave it to you to draw:

A downward sloping line with K on one axis and L on another that has a maximum capital of 12 and a maximum labor of 6.  Label the line c=120.

b.      If the marginal product of labor is 4, what is the marginal product of capital at an economically efficient point?  Why?

By the last dollar rule, (MPl/w) should equal (MPk/r).  So, I have (4/20)=(MPk/10) which means MPk = 2.  Can also do from the MRTS = input ratio, so that (MPk/MPl) should have the same ratio as (r/w), and that means (MPk/4)=(10/20).

c.       What values define the slope of an isocost?

The ratio of the input prices.

d.      Why can’t isocost lines cross each other?

It does not make any sense if they do.  It says there is a crossing point where they have the same cost, yet anywhere else there are two bundles that use the same amount of one input and two different amounts of the other input yet have the same cost.  That is just nutty.

6) Complete the following table for a long run cost function.

 a) Quantity of Output Total Cost Average Cost Marginal Cost 0 0 ------------ --------- 1 4 4 4 2 7 3.5 3 3 9.5 3.2 2.5 4 11.5 2.9 2 5 13.3 2.7 1.8 6 15.3 2.6 2 7 18.3 2.6 3 8 21.8 2.7 3.5

b. If the market price for the output produced is 2 and the market structure is perfectly competitive, what level of output is the profit maximizing level of output?  Why?

Here I can consider three points.  One: q=0, profit is zero.  Two: MC=2 at 4.  Here P is less than AC, so profit is 8-11.5 or -3.5.  Three:  q=6, here is still less than AC, so profit is 2*6-15.3=-3.3.

Zero q is the best of the three options.

7) You are given the following information on the relationship between inputs and production level at various points.

 Points Labor Capital Output A 2 1 4 B 4 2 12 C 8 4 24 D 16 8 35 E 32 16 40

a.  Illustrate these points using isoquants.

Again, let me describe.  Curved downward sloping lines on a K, L graph with points labeled A-E lined up on the quantities.  The labels of the downward sloping lines (the isoquants) have the output labels on them.

b. Contrast the returns to scale implied by movement between the points. (circle the correct answer)

From a to b I have (increasing, constant, decreasing) returns to scale.

From b to c I have (increasing, constant, decreasing) returns to scale.

From c to d I have (increasing, constant, decreasing) returns to scale.

From d to e I have (increasing, constant, decreasing) returns to scale.

8)      Production and cost functions. (2 points)

a.       You are given the following information.  Calculate marginal product for each change in input level.

 Input level Output level Marginal Product 0 0 NA 1 11 11 2 21 10 3 30 9 4 38 8 5 45 7 6 51 6 7 56 5 8 60 4 9 63 3

b.      Given your findings on marginal product in (a) and assuming input cost is constant, is the associated marginal cost curve:    downward sloping over input levels 0-9; upward sloping over input levels 0-9; upward sloping for some input levels and downward sloping for other input levels between 0 and 9?  Explain your reasoning.

Marginal cost is going to be upward sloping over input levels 0-9.  Marginal product is decreasing over this range, so it will take me more workers to generate one additional unit of output when I am at higher input levels due to diminishing marginal product which characterizes the production function.

c.       If the cost of the input of labor L is \$10 per unit, calculate the cost of producing each level of output, and the marginal cost for changing the output level.

 Input level L Output level Q Cost of producing Q Change in Q Change in cost Marginal Cost 0 0 0 NA NA NA 1 10 10 10 10 1 2 22 20 12 10 .83 3 31 30 9 10 1.1 4 40 40 9 10 1.1 5 48 50 8 10 1.25 6 55 60 7 10 1.43 7 61 70 6 10 1.67 8 66 80 5 10 2 9 70 90 4 10 2.5

 Statement The statement is (circle the correct answer) The slope of the isocost line is called the marginal rate of technical substitution. True            False Consumer surplus is calculated as the area under the demand curve and above the price line. True            False In a perfectly competitive market the firm is a price taker. True            False If where price = MC(q), price is less than average variable costs, the firm should produce output level q. True            False Marginal cost = cost of the input / marginal product. True            False The bisection rule allows us to derive the marginal cost curve from a linear demand curve. True            False For all monopolies, average cost is greater than marginal cost over the feasible range of output levels. True            False A necessary but not sufficient condition for economic efficiency is technologically efficiency. True            False

10)  Production.

a.       Define marginal product.

Change in the output divided by the change in the input required to generate this change in output.  MP=change in q/change in l for example.

b.      Define average product.

Output level divided by input level used to generate this output. AP=q/l for example

c.       Draw a production function with labor as the variable input, and that exhibits diminishing marginal returns to labor.

OUTPUT on the Y axis

Labor on the x axis

d.      If capital level is held fixed as you vary labor in (c), is what you drew a long run or short run production function?  Why?

Short run since there is a fixed input, as capital is being held fixed.