Question

A purely competitive wheat farmer can sell any wheat he grows for $30 per bushel. His five acres of land show diminishing returns because some are better suited for wheat production than others. The first acre can produce 1,000 bushels of wheat, the second acre 900, the third 800, and so on.

a. Use the table below to answer the following questions.
How many bushels will each of the farmer's five acres produce?
How much revenue will each acre generate?
What are the TR and MR for each acre?
Number of Acres That Acre's Yield That Acre's Revenue TR MR
0 -- $0 0 ---
1 1,000.00 30,000.00 30,000.00 ___
2 900.00 27,000.00 57,000.00 ___
3 800.00 24,000.00 81,000.00 ___
4 700.00 21,000.00 102,000.00 ___
5 600.00 18,000.00 120,000.00 ___
b. If the marginal cost of planting and harvesting an acre is $24,000 per acre for each of the five acres, how many acres should the farmer plant and harvest?

Answer 1

Answer:(a) I 8,000 bushel, 7,200 bushel, 6,400 bushel, 5,600 bushel, 4,800 bushel (ii) $240,000, $216,000, $192,000, $168,000, $144,000 (iii)TR = 30,000 ,27,000, 24,000,21,000,18,000, MR = 0, 27,000, 24,000, 21,000, 18,000 (b) in a purely competitive market the farmer will maximize profit where MC =MR, MC = MR at third acre,therefore the farmer should plant three acre

Step-by-step explanation:

calculate how many bushel will each of the farmer five acres produce

Since a bushel is 8 gallons of wheat

Gallons × Quantity produce

First acre = 8 × 1000 = 8,000

Second acre = 8 × 900 = 7,200

Third acre = 8 × 800 = 6,400

Fourth acre = 8 × 700 = 5,600

Fifth acre = 8 × 600 = 4,800

To calculate how much revenue will each acre generate

Since the price is $30 per bushel

= price × bushel produce

First acre = 30 × 8,000 = 240,000

Second acre = 30 × 7,200 = 216,000

Third acre = 30 × 6,400 = 192,000

Fourth acre = 30 × 5,600 = 168,000

Fifth acre = 30 × 4,800 = 144,000

To calculate the TR

= Price × Quantity

First acre = 30 × 1,000 = 30,000

Second acre = 30 ×900 = 27,000

Third acre = 30 × 800 = 24,000

Fourth acre = 30 × 700 = 21,000

Fifth acre = 30 × 600 = 18,000

To calculate MR

Change in Acres Revenue

First acre = 30,000 -30,000 =0

Second acre = 57,000 - 30,000 = 27,000

Third acre = 81,000 - 57,000 = 24,000

Fourth acre = 102,000 - 81,000 = 21,000

Fifth acre = 120,000 - 102,000 = 18,000

To calculate how many acres should the farmer plant and harvest

In a perfectly competitive market profit is maximized where MC = MR

Since the farmer is a purely competitive wheat farmer, therefore the farmer will maximize profit where MC = MR

Since the MC of planting and harvesting is $24,000 , therefore MC = MR at the third acre, The farmer should plant and harvest three acre of land.