Question

In: Economics

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

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

Expert Solution

Isoprofit lines are the set of curves on which combination of input and output gives the same amount of profit generated.

For year 2, price of gadgets is $3 and price of single variable input is $18.

At the profit maximizing level, quantity of input = 49 units and quantity of output = 588 units.

Thus profit generated = $3*588 - $18*49 = $882

Now consider all given options:

a)

use 15 units of input to produce 330 units of gadgets'

Profit generated = $3*330 - $18*15 = $720 < $882 (Feasible production plan)

b)

use 20 units of input to produce 400 units of gadgets

Profit generated = $3*400 - $18*20 = $840 < $882 (Feasible production plan)

c)

use 25 units of input to produce 450 units of gadgets

Profit generated = $3*450 - $18*25 = $900 > $882 (Not feasible production plan)

d)

use 30 units of input to produce 470 units of gadgets

Profit generated = $3*470 - $18*30 = $870 < $882 (Feasible production plan)

Hence production plans (a), (b) and (d) are feasible for (within the technology set of) a profit-maximizing gadget producer.

Rahul Sunny answered 1 year ago

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