National cement factor is engage in the production of cement, and the company has birr 10,000,000 birr. Further, the production function of the company is given by Q = 20L1/2K1/2, and the unit cost of labor and capital are birr 100 and 50 respectively. Given the above information perform the following questions. Determine the type of returns to scale that the company production function has? Find the optimal level of labor and capital, and maximum output? Find the level of profit if the unit price of 100 KM of cement is birr 400?

A production function refers to an equation that captures the highest number of output that can be manufactured with a limited or given set of input.

To determine whether a production function has growing, decreasing, or constant returns to scale, multiply each input with a positive constant (t > 0), then see if the entire production function is multiplied with a number that is higher, lower, or equal to that constant.

Recall the the production function is given as:

Q = 20L1/2K1/2; and

Unit cost of Labor and Capital are 100 and 50 respectively. Plugging the Unit costs of Labor and Capital respectively, we have:

Q = (20 * 100)/ (2 *50/2)

= 2000/50

Q = 40

Hence the production function of the company has a constant returns to scale.

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