Suppose a producer faces the following production function: K^0,5.K^0,5 given that L is the unit of labour and K is the unit of capital. Suppose K is 16, labour wage rate is R10 and rental rate of capital is R50, derive the TC and MC functions

Suppose a firm could produce data storage services using two inputs: high capacity hard drive (200 TB) or low capacity hard drive (100 TB).   What is the production function and what is a typical set of isoquant?

Consider the production function: Y = z.f(K,N,L) where Y is output, z is a parameter capturing technology, K is capital, N is labour and L is the area of land.

Suppose the production function for T-shirts can be represented as q =  L0.25 K0.75. Show that the production function has constant returns to scale.

A firm’s short-run production function is in the form of                        q = aLK +(bL^2)K −(cL^3)K , wherea, b, c > 0 are parameters. K is a constant. (a) Derive the marginal product of labor.(b) Find the level of L, expressed in terms of the parameters, at which the law ofdiminishing marginal product kicks in.

The production function for a product is given by q= 10K^(1/2)L^(1/2) where K is capital, and L is labor and q is output d)  Now suppose w =30 and r = 120. What is the minimum cost of producing q=1000. (You must show your work by clearly writing the equations that you use to derive the cost minimizing levels of L and K.) e)  Now suppose that the firm is in the short run and cannot vary the amount of capital. That is, it must use the same amount of capital as in part d). However, the firm wants to produce 1200 units of output. How much labor should it use to minimize its cost and what is the minimum cost of producing q =1200?

Consider a short run production function q=5L+K, using L units of labour and K units of capital. Compute the marginal product of labour.                                      2. Does the production function exhibit decreasing, increasing or constant returns to scale?