Suppose that labor is the only input used by a perfectly competitive firm that can hire workers for $50 per
day. The firm’s production function is as follows:
Days of Labor/Units of Output:
0/0, 1/7, 2/13, 3/19, 4/25, 5/28, 6/29, 7/29
c. Compute the demand schedule showing the number of workers hired for all wages from zero to $100 a day.
How Would this be done.
e. What happens to this demand curve if the price of output rises from $10 to $12 per unit?
Wouldn't the demand curve shift downward.
for c) you need more information, you need the price of the output. Can you assume the price is $10 per unit as suggested in e.?
Assuming output can be sold at 10 per unit, 1 worker can make $70 of output, 2 can make $130 (change=$60), 3 can make $190 (change=$60), and so on. Tada, graph the changes, and you have the firm's demand curve for workers. 100-70 hire zero, 70-60 hire 1, 60-30 hire 4, 30-20 hire 5, 20-00 hire 6.
e) if output price rises, firms will want to produce more, sow they will hire more labor, demand shifts outward.
Thank you for the information.
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To compute the demand schedule showing the number of workers hired for all wages from zero to $100 a day, we can use the given production function and assume the price of output is $10 per unit.
Step 1: Calculate the total output for each number of workers hired.
- With 0 workers, the output is 0 units.
- With 1 worker, the output is 7 units.
- With 2 workers, the output is 13 units.
- With 3 workers, the output is 19 units.
- With 4 workers, the output is 25 units.
- With 5 workers, the output is 28 units.
- With 6 workers, the output is 29 units.
- With 7 workers, the output is 29 units.
Step 2: Calculate the value of output for each level of production.
- With 0 units of output, the value is $0.
- With 7 units of output, the value is $70 ($10 per unit).
- With 13 units of output, the value is $130.
- With 19 units of output, the value is $190.
- With 25 units of output, the value is $250.
- With 28 units of output, the value is $280.
- With 29 units of output, the value is $290.
- With 29 units of output, the value is $290.
Step 3: Determine the number of workers hired for each wage level.
- From $0 to $70 per day, the firm will hire 0 workers.
- From $70 to $130 per day, the firm will hire 1 worker.
- From $130 to $190 per day, the firm will hire 2 workers.
- From $190 to $250 per day, the firm will hire 3 workers.
- From $250 to $280 per day, the firm will hire 4 workers.
- From $280 to $290 per day, the firm will hire 5 workers.
- From $290 to $290 per day, the firm will hire 6 workers.
So, the demand schedule showing the number of workers hired for all wages from zero to $100 a day would be as follows:
- For wages from $0 to $70 per day, the firm hires 0 workers.
- For wages from $70 to $130 per day, the firm hires 1 worker.
- For wages from $130 to $190 per day, the firm hires 2 workers.
- For wages from $190 to $250 per day, the firm hires 3 workers.
- For wages from $250 to $280 per day, the firm hires 4 workers.
- For wages from $280 to $290 per day, the firm hires 5 workers.
- For wages from $290 and above, the firm hires 6 workers.
Now, let's discuss what happens to the demand curve if the price of output rises from $10 to $12 per unit.
When the price of output rises, firms will have a higher incentive to produce more and increase their profit. As a result, they will want to hire more labor to increase production levels. This leads to a shift in the demand curve for labor outward, indicating an increase in the quantity of labor demanded at each wage level. So, the demand curve for workers will shift to the right when the price of output rises from $10 to $12 per unit.