Question

The firm's production function as reported by the firm's production engineer is as follows:

# of Labor Units may be employed per week	# of chairs may be produced
0	0
1	5
2	15
3	25
4	35
5	39
6	42
7	44
8	45

Moreover, the accounting department reports that the wage rate is $10, the unit cost of raw material is $1, the firm needs one (1) unit of raw material for each chair and the total fixed cost is $5.

- Find how many chairs the firm must produce and sell if the selling price of a chair is $3, or $5, or $8.

- Then draw a graph of a selling price and the corresponding quantities at each price to indicate the firm's supply line.

Answer 1

Labor employed	Quantity produced	Fixed Cost ($)	Variable Cost ($)	Total Cost ($)	Marginal Cost ($)
0	0	5	0	5	-
1	5	5	15	20	3.00
2	15	5	35	40	2.00
3	25	5	55	60	2.00
4	35	5	75	80	2.00
5	39	5	89	94	3.50
6	42	5	102	107	4.33
7	44	5	114	119	6.00
8	45	5	125	130	11.00

Variable Cost = # Labor employed * Wage rate + Output * unit cost of raw material = # Labor employed * $10 + Quantity produced * $1

Total Cost = Fixed Cost + Variable Cost

Marginal Cost of output at Nth worker = (Change in the TC from previous worker/Change in quantity produced form previous worker)

Profit-maximizing quantity: The maximum quantity up to which the marginal cost remains less than or equal to the price of each chair.

When P = $3, the profit-maximizing quantity i.e., the maximum quantity up to which the MC ≤ $3 is 35 chairs. Therefore, the firm must produce 35 chairs at a price of $3 per chair.

When P = $5, the profit-maximizing quantity i.e., the maximum quantity up to which the MC ≤ $5 is 42 chairs. Therefore, the firm must produce 42 chairs at a price of $5 per chair.

When P = $8, the profit-maximizing quantity i.e., the maximum quantity up to which the MC ≤ $8 is 44 chairs. Therefore, the firm must produce 44 chairs at a price of $8 per chair.

Supply curve of the firm: By doing a similar analysis at different prices, the supply curve of the firm is obtained as shown below