Suppose that the production function is given by,    Assuming that the price of x is $3 and the price of y is $4. Derive the corresponding VMP and AVP functions. What is MFC? Solve for the profit-maximizing level for input use x.

Let the production function of a firm is given as q=(x0.5 +y0.5)2 Where x and y are inputs and wx is the price of input x and wy is the price of input y. a) Assume the firm has a limited budget to spend on buying input. Find the cost-conditional input demand function for each input. b) Find the cost function of the firm.

Suppose a firm producing wood burning stoves has the following production function Q(K, L) = 4K¹/2 [1/2 Where L, the labour, and K, the capital are the 2 inputs of production and Q the quantity of stoves. Assume the price of one unit of L is £1 and the price of one unit of K is £2. a) b) Assume that K=9 in the short run. Draw the production function and calculate the marginal products of L as L changes from L= 1 to L= 6. What does an isoquant curve show? Draw the graph of a production isoquant representing input combinations that will produce 8 units of output.

In the following production function: f(x1, x2) = Ax1α1 x2α2 , where A, α1, α2 > 0. What is the marginal product of input 1?

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Suppose the production function is Cobb-Douglas and  f(x1;x2)=x11/2x23/2 Write an expression for the marginal product of x1. Does marginal product of x1 increase for small increases in x1, holding x2 fixed? Explain Does an increase in the amount of x2 lead to decrease the marginal product of x1? Explain What is the the technical rate of substitution between x2 and x1? What is the type of returns to scale of this production function? (Increasing, decreasing, constant)

Catalina Films produces video shorts using digital editing equipment (K) and editors (L). The firm has the production function Q(K, L)=KxL, where Q is the hours of edited footage. The wage is $25, and the rental rate of capital is $50. The firm wants to produce 3,000 units of output at the lowest possible cost. a) Find the marginal product of each input. b) Determine whether the production function exhibits diminishing marginal product to each input. c) Find the marginal rate of technical substitution (MRTSLK) d) How does MRTSLK change as more L, is used holding output constant. e) Find the least costly combination of labour and capital to produce 3000 units.

Catalina Films produces video shorts using digital editing equipment (K) and editors (L). The firm has the production function Q(K, L)=KxL, where Q is the hours of edited footage. The wage is $25, and the rental rate of capital is $50. The firm wants to produce 3,000 units of output at the lowest possible cost.a) Find the marginal product of each input.b) Determine whether the production function exhibits diminishing marginal product to each input.c) Find the marginal rate of technical substitution(MRTSLK)d) How does MRTSLK change as more L, is used holding output constant.e) Find the least costly combination of labor and capital to produce 3000 units

To produce a recorded DVD, a firm uses one blank disk D and the services of a recording machine M for one hour. The production function in this case is given by: Q = min{D, M}(a) Using this production function, find the firm’s demand function for recording machine-hours M.(b) ) Draw the total product, average product, and marginal product of M curves for the production function identified(c) Let PM denote the hourly price of renting the recording machine M and PD denote the price of one blank disk. Use your answer from (b) to calculate the firm’s short-run total, average, and marginal cost functions.

A firm has the production function y=4z₁​+10z₂. Input prices are w₁=5 and w₂=6. a) What is the cost minimizing input bundle?