Download DETAILED ANSWRES for the Econ 100 FALL 2014, October 20 In

DETAILED ANSWRES for the Econ 100 FALL 2014, October 20 In-class exercise: The supply schedule of a small firm
Start with 0 t-shirts.
Ask:
“Should we produce one more t-shirt?”
Answer:
“YES” if marginal benefit of the first t-shirt > marginal cost of the first t-shirt,
“NO” if otherwise.
The marginal benefit of the first t-shirt is the price offered by Benetton, the marginal cost is worker’s hourly wage +
cost of materials.
Repeat the question “Should we produce one more t-shirt?” as long as the answer has been “YES”.
Stop when the answer is “NO” for the first time. The number of t-shirts where you have stopped is the optimal (or
the best, or the profit maximizing) level.
THIS IS VERSION 1
A small t-shirt factory uses one machine (leased at 300TL a week) to produce t-shirts. The machine is operated by
one worker and produces 1 t-shirt per hour. The worker is paid 10TL per hour on weekdays, 20TL per hour on
Saturdays, and 30TL per hour on Sundays. Working day is max 10 hours by law. The law is strictly enforced. All other
costs, such as raw materials, electricity, etc., are 5TL per t-shirt.
Benetton is the only buyer of t-shirts from our small factory. They will buy as many as the factory can supply.
Production Costs in Version 1
Wage rata per hour
10TL weekdays
20TL on Saturday
30TL on Sunday
Material costs 5TL
BENETTON offers P = 10TL per t-shirt
Marginal benefit is 10TL
Marginal cost of the first t-shirt is 10 + 5 = 15, the answer is NO you stop at 0.
BENETTON offers P = 20TL per t-shirt
Marginal benefit is 20TL
Marginal cost of the first t-shirt is 10 + 5 = 15, the answer is YES for the first t-shirt and for additional 49 t-shirts.
When you produced your 50th t-shirt and ask the question “should we produce one more t-shirt?”, you will see that
the marginal cost is now 20 + 5 = 25, so the answer is NO. You stop at 50.
BENETTON offers P = 30TL per t-shirt
Marginal benefit is 30TL
Marginal cost of the first t-shirt is 10 + 5 = 15, the answer is YES for the first t-shirt and for additional 49 t-shirts.
When you produced your 50th t-shirt and ask the question “Should we produce one more t-shirt?” the marginal cost
is 20 + 5 = 25, so the answer is still YES. The answer is also YES for the next 9 t-shirts. When you produced your 60th
t-shirt and ask the question “should we produce one more t-shirt?”, you will see that the marginal cost is now 30 + 5
= 35, so the answer is NO. You stop at 60.
BENETTON offers P = 40TL per t-shirt
Marginal benefit is 40TL
The highest marginal cost is for the t-shirts you produce on Sundays, that is the t-shirts 61, 62, until 70.
The marginal cost of these each of last 10 t-shirts is 30+5 = 35, which is less than the marginal benefit when
BENETTON’s buying price is 40TL.
The answer is YES for all 70 t-shirts. You will stop at 70 because this is your maximum production capacity.
BENETTON offers P = 50TL per t-shirt
Marginal benefit is 50TL
Same as above: You stop at 70 because this is your maximum production capacity.
Now we will construct the supply schedule. Quantity supplied as a function of the price Benetton offers
Price
10TL
20TL
30TL
40TL
50TL
Quantity supplied
0
50
60
70
70
Draw a price-quantity supplied graph: put these price and quantity supplied numbers on the graph and connect the
dots with a line. What is the shape of the line?
THIS IS VERSION 2
A small t-shirt factory uses one machine (leased at 300TL a week) to produce t-shirts. The machine is operated by
one worker and produces 1 t-shirt per hour. The worker is paid 10TL per hour on weekdays, 20TL per hour on
Saturdays, and 30TL per hour on Sundays. Working day is max 10 hours by law. The law is strictly enforced. All other
costs, such as raw materials, electricity, etc., are 15TL per t-shirt.
Benetton is the only buyer of t-shirts from our small factory. They will buy as many as the factory can supply.
Production Costs in Version 2
Wage rata per hour
10TL weekdays
20TL on Saturday
30TL on Sunday
Material costs 15TL
BENETTON offers P = 10TL per t-shirt
Marginal benefit is 10TL
Marginal cost of the first t-shirt is 10 + 15 = 25, the answer is NO you stop at 0.
BENETTON offers P = 20TL per t-shirt
Marginal benefit is 20TL
Marginal cost of the first t-shirt is 10 + 15 = 25, the answer is NO, you stop at 0 again.
BENETTON offers P = 30TL per t-shirt
Marginal benefit is 30TL
Marginal cost of the first t-shirt is 10 + 15 = 25, the answer is YES for the first t-shirt and for additional 49 t-shirts.
When you produced your 50th t-shirt and ask the question “should we produce one more t-shirt?”, you will see that
the marginal cost is now 20 + 15 = 35, so the answer is NO. You stop at 50.
BENETTON offers P = 40TL per t-shirt
Marginal benefit is 40TL
Marginal cost of the first t-shirt is 10 + 15 = 25, the answer is YES for the first t-shirt and for additional 49 t-shirts.
When you produced your 50th t-shirt and ask the question “Should we produce one more t-shirt?” the marginal cost
is 20 + 15 = 35, so the answer is still YES. The answer is also YES for the next 9 t-shirts. When you produced your 60th
t-shirt and ask the question “should we produce one more t-shirt?” you will see that the marginal cost is now 30 + 15
= 45, so the answer is NO. You stop at 60.
BENETTON offers P = 50TL per t-shirt
Marginal benefit is 50TL
The highest marginal cost is for the t-shirts you produce on Sundays, (the t-shirts 61, 62, … until 70).
The marginal cost of each of these last 10 t-shirts is 30+15 = 45, which is less than the marginal benefit when
BENETTON’s buying price is 50TL.
The answer is YES for all 70 t-shirts. You will stop at 70 because this is your maximum production capacity.
Now we will construct the supply schedule. Quantity supplied as a function of the price Benetton offers
Price
10TL
20TL
30TL
40TL
50TL
Quantity supplied
0
0
50
60
70
Draw a price-quantity supplied graph: put these price and quantity supplied numbers on the graph and connect the
dots with a line. What is the shape of the line?
The two supply curves together: The blue supply curve one is for version 2 where raw materials cost 15TL per t-shirt
The yellow-brown is supply curve one is for version 1 where raw materials cost 5TL per t-shirt. With lower input
prices the supply shifts to the right
They touch when P = 50, because at that price the firm hits the capacity constraint of 70 t-shirts.