In YEAR 1, the price of gadgets is $2, while the price of the single variable input used is $28.

A profit-maximizing gadget producer uses 9 units of input to produce and sell 252 units of gadgets, earning profit of $2*252 - $28*9 = $252

In YEAR 2, the price of gadgets is $3, while the price of the single variable input used is $18.
A profit-maximizing gadget producer uses 49 units of input to produce and sell 588 units of gadgets, earning profit of $3*588 - $18*49 = $882


A production plan is feasible if it lies BELOW a firm's iso-profit lines.

Which of the following production plans (input-output combinations) are feasible for (within the technology set of) a profit-maximizing gadget producer?

(a) use 15 units of input to produce 330 units of gadgets
(b) use 20 units of input to produce 400 units of gadgets
(c) use 25 units of input to produce 450 units of gadgets
(d) use 30 units of input to produce 470 units of gadgets


Question 11 options:

1) all of the production plans are feasible

2) plans (a), (b) and (c) are feasible, plan (d) is NOT feasible

3) plans (a), (b) and (d) are feasible, plan (c) is NOT feasible

4) plans (a), (c) and (d) are feasible, plan (b) is NOT feasible

5) plans (b), (c) and (d) are feasible, plan (a) is NOT feasible

6) two of the plans are feasible, two are NOT feasible

7) only plan (a) is feasible, plans (b) , (c) and (d) are NOT feasible

8) only plan (b) is feasible, plans (a) , (c) and (d) are NOT feasible

9) only plan (c) is feasible, plans (a) , (b) and (d) are NOT feasible

10) only plan (d) is feasible, plans (a) , (b) and (c) are NOT feasible

11) NONE of the production plans are feasible

To determine which production plans are feasible for a profit-maximizing gadget producer, we need to compare each plan's profit to the iso-profit line.

The formula for profit is given by:
Profit = (price of gadgets * quantity of gadgets) - (price of input * quantity of input)

Let's calculate the profit for each production plan and compare it to the profit earned in YEAR 1 and YEAR 2.

(a) Plan: use 15 units of input to produce 330 units of gadgets
Profit = ($3 * 330) - ($18 * 15) = $990 - $270 = $720

(b) Plan: use 20 units of input to produce 400 units of gadgets
Profit = ($3 * 400) - ($18 * 20) = $1,200 - $360 = $840

(c) Plan: use 25 units of input to produce 450 units of gadgets
Profit = ($3 * 450) - ($18 * 25) = $1,350 - $450 = $900

(d) Plan: use 30 units of input to produce 470 units of gadgets
Profit = ($3 * 470) - ($18 * 30) = $1,410 - $540 = $870

Now, let's compare these profits to the profits earned in YEAR 1 and YEAR 2.

In YEAR 1, the profit was $252.
In YEAR 2, the profit was $882.

Comparing the profits, we can see that:
- Plan (a) has a higher profit than both YEAR 1 and YEAR 2.
- Plan (b) has a lower profit than YEAR 2 but higher than YEAR 1.
- Plan (c) has a higher profit than YEAR 2 but lower than YEAR 1.
- Plan (d) has a lower profit than both YEAR 1 and YEAR 2.

Based on the above comparisons, we can conclude that:
- Plan (a) is feasible.
- Plan (b) is not feasible.
- Plan (c) is not feasible.
- Plan (d) is not feasible.

Therefore, the correct answer is:
3) plans (a), (b) and (d) are feasible, plan (c) is NOT feasible.

To check which production plans are feasible for a profit-maximizing gadget producer, we need to compare the profit earned from each plan with the profits earned in Year 1 and Year 2.

Let's calculate the profit for each production plan:

(a) Use 15 units of input to produce 330 units of gadgets:
Profit = ($3 * 330) - ($18 * 15) = $990 - $270 = $720

(b) Use 20 units of input to produce 400 units of gadgets:
Profit = ($3 * 400) - ($18 * 20) = $1200 - $360 = $840

(c) Use 25 units of input to produce 450 units of gadgets:
Profit = ($3 * 450) - ($18 * 25) = $1350 - $450 = $900

(d) Use 30 units of input to produce 470 units of gadgets:
Profit = ($3 * 470) - ($18 * 30) = $1410 - $540 = $870

Comparing these profits with the profits earned in previous years:

In Year 1, the profit was $252.
In Year 2, the profit was $882.

Based on this information, we can determine the feasible production plans:

- Plan (c) is feasible with a profit of $900, which is higher than the profits earned in both Year 1 and Year 2.
- Plan (b) is also feasible with a profit of $840, which is higher than the profit earned in Year 1, but lower than the profit earned in Year 2.

Therefore, the correct answer is:
3) plans (a), (b), and (d) are feasible, plan (c) is NOT feasible