onsider the production functionQ = 100K3/4L1/5where Q is the quantity of goods produced, K is the capital and L is thelabour.(a) Find the value of Q when K = 81 and L = 32.(b) What happens to the value of Q if we halve the labour and capital?(c) Find an expression for ln Q in terms of ln K and ln L

A firm's production function is given by Q = 5K^0.5L^0.5, where Q is output, K is capital, and L is labor. If the firm uses 9 units of capital (K) and 16 units of labor (L), calculate the level of output (Q)

A manufacturer determines that m employees will produce a total of q units each week. The relation between the number of employees and the quantity is given as: 𝑞 = 5𝑚2 + 2𝑚 + 4. Given that the demand function for the product is given as 𝑝 = 1000 𝑞+8 , determine a. The rate of change of price with respect to quantity b. The rate of change of price with respect to the number of employees c. Determine the marginal revenue when the number of employees is 15

Consider a firm with production function given by 𝑄(𝐾, 𝐸) = 𝐾^1/3𝐸^2/3 K denotes units of capital and E denotes units of labour. Capital is fixed at 27 units. The firm’s output decision has no effect on the price of output or the wage (w). (a) The firm is profit maximizing and can sell output for $12 per unit. Solve for the firm’s labour demand function. That is, express E as a function of w. Note that for this production function, the marginal product of labour (MPL= MP_e) is MP_E = 𝜕Q(𝐾, 𝐸)/𝜕E = 2/3 𝐾^1/3𝐸^−1/3 Show your formulations and derivation.

he production function of a chocolate factory is given byQ = 100Le−0.25Lwhere L denotes the amount of labour and Q is the quantity of chocolate barsproduced.(a) Compute the first derivative dQdL .(b) Compute the second derivative d2QdL2 .(c) Find the value of L that maximizes the output Q

With reference to the given production function, calculate the quantity ofgood x that will be produced if the firm uses:a) 9 units of labour and 16 units of capital.