AP and MP of Labour:

AP of Labour:
- AP of labour refers to the average product of labour.
- It is the total output produced by all units of labour employed, divided by the number of units of labour employed.
- The formula for AP of labour is APL = Q/L, where Q is the total output produced and L is the units of labour employed.
- In this case, the production function is Q(L,K) = L¾K¼, assuming capital is fixed.
- Therefore, AP of labour can be calculated as APL = (L¾K¼)/L = K¼L-¼.

MP of Labour:
- MP of labour refers to the marginal product of labour.
- It is the additional output produced by employing one more unit of labour, while keeping all other inputs constant.
- The formula for MP of labour is MPL = ΔQ/ΔL, where ΔQ is the change in output produced and ΔL is the change in units of labour employed.
- In this case, the production function is Q(L,K) = L¾K¼, assuming capital is fixed.
- Therefore, MP of labour can be calculated as MPL = ∂Q/∂L = ¾K¼L-¼.

Difference between Budget Set and Budget Constraint:
- Budget Set refers to the set of all possible combinations of goods and services that can be purchased with a given income and prices.
- It includes all combinations of goods and services that lie within the budget constraint and those that lie outside it but are unaffordable.
- Budget Set can be represented graphically as a set of points within the budget constraint line.
- Budget Constraint refers to the line that represents all possible combinations of goods and services that can be purchased with a given income and prices.
- It is the boundary of the budget set and represents the combinations of goods and services that exhaust the income.
- Budget Constraint can be represented graphically as a straight line with slope equal to the ratio of the prices of two goods.

To determine the optimal capital-labor ratio set the marginal rate of technical substitution equal to the ratio of the wage rate to the rental rate of capital: K L = 30 120 , or L = 4K. Substitute for L in the production function and solve where K yields an output of 1,000 units: 1,000 = (100)(K)(4K), or K = 1.58.