Economics 101 L

Homework No. 8 Key

(due in lab on Oct. 27, 2008)

WORTH 100 POINTS TOTAL

  1. The following table contains data corresponding to a competitive firm that uses corn to produce chicken.WORTH 30 POINTS

Corn
(tons) / Chicken
(tons)
3,000 / 1,550
4,000 / 2,500
5,000 / 3,300
6,000 / 3,950
7,000 / 4,400
8,000 / 4,700
9,000 / 4,900
10,000 / 5,000

a. Assume that the firm can sell chicken at $300/tn:

i. Complete the following table by calculating the firm’s total revenue and marginal revenue product curves.6 points

Corn
(tons) / Chicken
(tons) / Total Revenue
($) / Marginal Revenue Product
($/tn of corn)
3,000 / 1,650 / 495,000
4,000 / 2,500 / 750,000 / 255
5,000 / 3,300 / 990,000 / 240
6,000 / 3,950 / 1,185,000 / 195
7,000 / 4,400 / 1,320,000 / 135
8,000 / 4,700 / 1,410,000 / 90
9,000 / 4,900 / 1,470,000 / 60
10,000 / 5,000 / 1,500,000 / 30

ii. If the firm must pay $90/tn of corn, how much corn will it use?

The firm will use 8,000 tons of corn, because that is where the marginal revenue product of corn equals the price of corn. 2 points

iii. If the price of corn drops to $60 per ton, how much corn will it use?

The firm will increase corn usage to 9,000 tons, because that is where the marginal revenue product of corn equals the price of corn. 2 points

iv. If the price of corn increases to $135 per ton, how much corn will it use?

The firm will reduce corn usage to 7,000 tons, because that is where the marginal revenue product of corn equals the price of corn. 2 points

b. Now suppose that the price of chicken falls to $200 per ton.

  1. Complete the following table by calculating the firm’s total revenue and marginal revenue product curves. 6 points

Corn
(tons) / Chicken
(tons) / Total Revenue
($) / Marginal Revenue Product
($/tn of corn)
3,000 / 1,650 / 310,000
4,000 / 2,500 / 500,000 / 190
5,000 / 3,300 / 660,000 / 160
6,000 / 3,950 / 790,000 / 130
7,000 / 4,400 / 880,000 / 90
8,000 / 4,700 / 940,000 / 60
9,000 / 4,900 / 980,000 / 40
10,000 / 5,000 / 1,000,000 / 20
  1. If the firm must pay $90/tn of corn, how much corn will it use?2 points

The firm will use 7,000 tons of corn, because that is where the marginal revenue product of corn equals the price of corn.

  1. If the price of corn drops to $60 per ton, how much corn will it use? 2 points

The firm will increase corn usage to 8,000 tons, because that is where the marginal revenue product of corn equals the price of corn.

  1. If the price of corn increases to $135 per ton, how much corn will it use?2 points

The firm will reduce corn usage to 6,000 tons, because that is where the marginal revenue product of corn equals the price of corn.

c. In a graph with corn in the horizontal axis and price and marginal revenue product (MRP) in the vertical axis, draw the firm’s demand for corn when the price of chicken is $300/tn and when the price of chicken is $200/tn. How does the fall in the price of chicken affect the firm’s demand for corn?6 points


The firm’s demand for corn is given by its MRP curve. Clearly, the fall in the price of chicken reduces the demand for corn.

2. A poultry producer’s short-run production is given in the following table:WORTH 40 POINTS

Input
(units of corn) / Output
(units of chicken) / Average Product
(units of chicken per unit of corn) / Marginal Product
(units of chicken per unit of corn)
0 / 0 / 0 / ------
1 / 7 / ------
2 / 18 / ------
3 / 33 / ------
4 / 50 / ------
5 / 65 / ------
6 / 78 / ------
7 / 87.5 / ------
8 / 92 / ------
9 / 92.7 / ------

The price per unit of corn is $10. In addition, the poultry producer has fixed costs of $30.

aCalculate the marginal product and the average product for each level of corn usage.5 POINTS

See table below

bGraph the marginal product and average product curves calculated in (a) with input on the horizontal axis:5 POINTS

c. In the graph constructed in (b), identify the regions with increasing marginal product and with diminishing marginal product.3 POINTS

Increasing marginal product from corn usage 0 to 4 units.

d. Calculate the firm’s total fixed cost (TFC), total variable cost (TVC), and total cost (TC) of producing chicken.5 POINTS See table below

e. Calculate the firm’s marginal cost (MC), average fixed cost (AFC), average variable cost (AVC), and average total cost (ATC) of producing chicken.5 POINTS - See table below

f. Graph AFC, AVC, ATC, and MC calculated in (e):5 POINTS - See graph below.

g. Suppose that the market for chicken is perfectly competitive, and that the price of chicken is $2.10 per unit.

  1. What is the firm’s marginal revenue? $2.10-4 POINTS
  2. Add a column for marginal revenue product (MRP) and compute for each level of input.

4 POINTS - See table.

  1. How many chicken units should the firm produce to maximize profits?4 POINTS

Should be some where between 87.5-92

  1. The graph below illustrates a hypothetical competitive firm facing varying prices in the market for wheat where annual output is graphed on the horizontal axis and the price of wheat is on the vertical axis.WORTH 30 POINTS

a)On graph paper, draw the firm’s short run supply curve remembering to consider shut down price. Also remember to label your axes.4 POINTS

b)What is the firm’s shut down price (i.e. Below what price will this firm produce no wheat in the short run)?3 POINTS

$3.00

c)Calculate the economic profit (or loss) when price is at P2.4 POINTS

-$6,000 (6-4 * (3,000))

d)Calculate the economic profit (or loss) when price is at P3.4 POINTS

$2,500 (6-5.50 * (5,000))

e)Below what price will short run economic profits be negative for this firm?3 POINTS

$5.00

f)How much wheat will be produced in the short run if price is P2?3 POINTS

3,000 bushels

g)At which price(s) will firms enter the market?3 POINTS

P3

h)At which price(s) will firms exit the market?3 POINTS

P1, P2

i)What is the long run equilibrium price in the market for wheat (assuming the industry is perfectly competitive)? What are economic profits at this price?3 POINTS

$5.00 – There is 0 economic profit at $5.00 per bushel.