A farmer can grow wheat or corn. The unit profits for a bushel of each are the same. To grow wheat (W) and corn (C), the farmer requires four input factors: Capital (K), land (L), A-Fertilizer (A), and B-fertilizer (B). The production of one bushel of corn requires two units of capital and the production of one unit of wheat four units of capital. The farmer has 32 units of capital available.The production of one bushel of corn requires two units of land and the production of one unit of wheat one unit of land. The farmer has 20 units of land available.The production of one bushel of corn requires two units of A-Fertilizer, and no B-fertilizer. The farmer has 18 units A-Fertilizer available.The production of one bushel of wheat requires one unit of B fertilizer, and no A-fertilizer. The farmer has 6 units of B-Fertilizer available. The farmer wants to maximize profits.1: Which formula describes the Fertilizer B constraint?aW ≤ 18bC ≤ 18cC ≤ 9dW≤62: The iso-profit line has a slope of negativea0.5b3c2d13: The optimum solution consists of how many bushels of corn?a8b9c4d74: The optimum solution consists of how many bushels of wheat?a4b9c8d75: If the unit profit for bushels of corn and bushels of wheat is each $1, then total profit is equal toa11b12c10d136: The shadow price (the increase in total profit) of relaxing the A-Fertilizer constraint by one unit isa0b1c2d47: The shadow price (the increase in total profit) of relaxing the B-Fertilizer constraint by one unit isa4b2c0d1

Given: Capital (K), land (L), A-Fertilizer (A), and B-fertilizer (B) The production of one bushel…

Answered: A farmer can grow wheat or corn. The…

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter11: Profit Maximization

Section: Chapter Questions

Problem 11.14P

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A farmer can grow wheat or corn. The unit profits for a bushel of each are the same. To grow wheat (W) and corn (C), the farmer requires four input factors: Capital (K), land (L), A-Fertilizer (A), and B-fertilizer (B).

The production of one bushel of corn requires two units of capital and the production of one unit of wheat four units of capital. The farmer has 32 units of capital available.
The production of one bushel of corn requires two units of land and the production of one unit of wheat one unit of land. The farmer has 20 units of land available.
The production of one bushel of corn requires two units of A-Fertilizer, and no B-fertilizer. The farmer has 18 units A-Fertilizer available.
The production of one bushel of wheat requires one unit of B fertilizer, and no A-fertilizer. The farmer has 6 units of B-Fertilizer available.

The farmer wants to maximize profits.

1: Which formula describes the Fertilizer B constraint?

a	W ≤ 18
b	C ≤ 18
c	C ≤ 9
d	W≤6

2: The iso-profit line has a slope of negative

a	0.5
b	3
c	2
d	1

3: The optimum solution consists of how many bushels of corn?

a	8
b	9
c	4
d	7

4: The optimum solution consists of how many bushels of wheat?

a	4
b	9
c	8
d	7

5: If the unit profit for bushels of corn and bushels of wheat is each $1, then total profit is equal to

a	11
b	12
c	10
d	13

6: The shadow price (the increase in total profit) of relaxing the A-Fertilizer constraint by one unit is

a	0
b	1
c	2
d	4

7: The shadow price (the increase in total profit) of relaxing the B-Fertilizer constraint by one unit is

a	4
b	2
c	0
d	1

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