You are given the following short-run production function for Superfast Hairdryers, Inc., where X is material inputs, and Q is output. Q = 10X - 0.25X2 Suppose the hair dryers are sold for $10 per unit to K-Mart. Also assume that the firm can obtain as much of the variable materials, input (X), as it needs at $20 per unit.
i) Determine the Marginal Revenue Product (MRP) of materials.
ii) Determine the Marginal Cost (MC) function.
iii) Determine the optimal value of X, given the objective, is to maximise profit.
iv) If the price of hair dryers were to rise, what happens to the optimal values of X employed to produce the hair dryers?
v) If the quantity of capital were to rise, what would happen to the Marginal Product (MP) of materials?
You are given the following short-run production function for Superfast Hairdryers, Inc., where X is material...
Consider the following short-run production function (where L = variable input, Q = output): Q=6L−0.4L2 Suppose that output can be sold for $10 per unit. Also assume that the firm can obtain as much of the variable input (L) as it needs at $20 per unit. What is the marginal revenue product function (MRPL)? $20 $60−$8L $10 $6−$0.40L What is the marginal factor cost function (MFCLMFCL)? $6−$0.40L $60−$8L $10 $20 What is the optimal value of L, given that the...
Q5. Given the following short-run production function (x = variable input, Q = output): Q = 3x2 - 0.1x3 (a) Determine the marginal product function (MPx) and the average product function (APx ). (b) Find the value of x that maximizes Q. (c) Find the value of x for which MPx is maximum. (d) Find the value of x for which APx is maximum. (e) Determine the boundaries of the three...
Suppose in the short run a firm’s production function is given by Q = L1/2*K1/2, and that K is fixed at K = 36. If the price of Labor, w = $12 per unit of Labor, what is the firm’s Marginal Cost of production when the firm is producing 48 units of output? MC = ________________________
Suppose that a firm's production function is q = 5x0.5 in the short run, where there are fixed costs of $2,000, and x is the variable input whose cost is S1250 per unit. What is the total cost of producing a level of output q? In other words, identify the total cost function C(q) The total cost of producing a level of output q is O A. C(g)-2,000. ca-2,000+ C(q) = 2,000 + Cla)= 800 O B. 25 % C....
You are given the following production function Q = K1/3L2/3, where Q is output, L is labor, and K is capital. First, calculate the marginal product of capital and the marginal product of labor. Next, calculate the marginal rate of technical substitution of labor for capital, MRTSL,K. What does this tell you about the production function?
5) A firm's short-run production function is given by Q=50 L-.02 L^{2}Where L denotes the number of workers.1. Find the size of the workforce that maximizes output.2. Find marginal product of labor (M PL)3. Find the average product of labor (APL)4. Find the size of the workforce which maximizes the average product of labor. Calculate M PL and A PL at this value. What do you observe.6) Find and classify the critical (stationary) points of the following function and state...
7. Assume that the long-run production function can be expressed as Q-SKL? Where Q is quantity of output, K is the quantity of capital and L is the quantity of labor. If capital is fixed at 10 units in the short run then the short-run production function is: Q=10KL b. Q=50KL? Q=10L? d. 0=50L Q=500KL 8. For a linear total cost function: a. MC will be downward sloping b. MC = AVC c. AVC is upward sloping and linear d....
Short-Run Market Supply. New England Textiles, Inc., is a medium-sized manufacturer of blue denim that sells in a perfectly competitive market. Given $25,000 in fixed costs, the total cost function for this product is described by TC $25,000 $1Q S0.000008 Q Mc= aTCaQ = $1 + $0.00001 6Q where Q is square yards of blue denim produced per month. Assume that MC> AVC at every point along the firm's marginal cost curve, and that total costs include a normal profit....
asput. A firm has the following production function. y=f(x) where y is the output and is the input, if the price of y is 521 unit and the price of x is 56/ unit, complete the following table and plot output, AP. and MP on graph paper and determine the optimum level of the input x that should be used to maximize profit, given Fixed Costs = 5100. - INPUT ----0 - -TR.. .TC__ -11. 1 OUTPUT - AP- -...
Q=F(X, X2. X3) Suppose that your manufacturing firm has the following production function with three inputs: are the three inputs. where X1, X2, and X3 Let MPx1 be the marginal product of X1, Px1 the cost of X1, MPx2 the marginal product of X2, Px2 the cost of X2, and so on. As a manager, which of the following equations will you use to determine the cost-minimizing quantities of X1 and X2 if the quantity of X3 is fixed? MPX1...