Suppose the economy consists of two types of firms: Type A firms which produce output using a technology Qa=Min(K,1/2L) and Type B firms which produce output using the technology Qb=Min(K,L). The economy has exactly forty units of labor and thirty units of capital. If we assume that all resources are fully employed, how much of good A will be produced? HOw much of good B?
To determine the amount of good A and good B produced, we need to calculate the output for Type A and Type B firms separately using the given technologies and resource constraints. Let's go step by step:
1. Determine the number of workers and capital allocated to each type of firm:
- Given that the economy has 40 units of labor, this will be fully allocated to both types of firms.
- Given that the economy has 30 units of capital, this will also be fully allocated to both types of firms.
2. Calculate the output for Type A firms:
The technology for Type A firms is Qa = Min(K, 1/2L)
- Here, K represents the units of capital allocated to Type A firms, which is the entire 30 units in the economy.
- L represents the units of labor allocated to Type A firms, which is also 40 units in the economy.
- Since Qa = Min(K, 1/2L), we take the minimum of the two inputs: Min(30, 1/2 * 40) = Min(30, 20) = 20.
- Therefore, Type A firms will produce 20 units of good A.
3. Calculate the output for Type B firms:
The technology for Type B firms is Qb = Min(K, L)
- Here, K represents the units of capital allocated to Type B firms, which is the entire 30 units in the economy.
- L represents the units of labor allocated to Type B firms, which is also 40 units in the economy.
- Since Qb = Min(K, L), we take the minimum of the two inputs: Min(30, 40) = 30.
- Therefore, Type B firms will produce 30 units of good B.
In summary:
- 20 units of good A will be produced by Type A firms.
- 30 units of good B will be produced by Type B firms.
To determine how much of good A and good B will be produced, we need to calculate the production levels for each type of firm based on the given technology.
1. Type A firms produce output using the technology Qa = Min(K, 1/2L). Since we have 40 units of labor available, we need to check if this constraint affects production.
a) Labor constraint: Since the technology uses half of the labor available, the maximum output is limited by the labor constraint. Thus, the production of good A for type A firms is Qa = Min(K, 1/2L) = Min(30, 1/2 * 40) = Min(30, 20) = 20 units.
2. Type B firms produce output using the technology Qb = Min(K, L). Again, we need to check if the constraints affect production.
a) Labor constraint: Since the technology uses all the available labor, the maximum output is limited by the labor constraint. Thus, the production of good B for type B firms is Qb = Min(K, L) = Min(30, 40) = 30 units.
Therefore, in this economy, 20 units of good A and 30 units of good B will be produced.