McPeak                                                           Name:____________________________

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 23 2 33 3 33 4 58 5 14 6 87

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

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

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

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?

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

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

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

3)      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?

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

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 Producer Surplus Total Social Welfare

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.

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

c.       What values define the slope of an isocost?

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

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 2 7 3 2.5 4 2 5 1.8 6 2 7 18.3 8 21.8

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?

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.

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 2 21 3 30 4 38 5 45 6 51 7 56 8 60 9 63

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.

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 2 22 3 31 4 40 5 48 6 55 7 61 8 66 9 70

9)      Circle the correct answer.

 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.

b.      Define average product.

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

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?