Suppose a firm has a production function as follows: y = 4x 25 x25, The price of x1 and x2 are 2 and 4, respectively. The demand for input 1 is:
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- Consider a production function in such a form: Q= f (K,L)= 3KL Calculate the elasticity of substitution (Ϭ) for this firm.Suppose that the production function is given by y = 2x0.5 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.What effect will a reduction in commodity price have on the input demand curve of the firm
- A firm produces basketballs with two variable inputs - labour (L) and plastic (K) - and has the following production function: f (L , K) = 6L1/3K1/6 If the price of output is 4, the price of labour is $2 and the price of plastic is $3, calculate the a) profit-maximizing level of each input b) the total production and c) the profit.Consider the following production function: y = lnx1 + lnx2, where x1>0, x2>0. Is it homogenous? Is the input requirement set monotonic and convex? Find its elasticity of substitution.Assume that you have a production function f(x, y) = √x + ln(y). The marginalproduct with respect to y is 1y.• True• False Please explain!
- The production function of a firm is f(x, y) = x + y. The marginal product of input xdiminishes with an increase of x.• True• False Please explain!Consider a firm that produces widgets according to the following Cobb-Douglas production function: Q = A * L^α * K^β where: Q is the quantity of output, L is the quantity of labor, K is the quantity of capital, A is a scale parameter (total factor productivity), α and β are the output elasticities of labor and capital respectively. Given that A = 1, α = 0.6, β = 0.4, L = 16 and K = 9, a) Calculate the quantity of output Q. b) If the firm increases the quantity of labor (L) to 20 while keeping the quantity of capital (K) constant, what will be the new quantity of output?The production function of a competitive firm is described by the equation y = 2x11/2 6x21/2. The factor prices are p1 = $3 and p2 = $4 and the firm can hire as much of either factor it wants at these prices. What is the firm’s marginal cost?
- Question 18 Consider a firm that has production function f(L,K)=4L2/3K1/3. What is the expression for this firm’s Marginal Product of labor? MPL(L,K)= 2K2/3/3L2/3. MPL(L,K)= 2K2/3/L1/3. MPL(L,K)= 2K1/3/3L1/3. MPL(L,K)= 5K2/3/3L2/3. MPL(L,K)= 8K1/3/3L1/3.A firm faces a production function given byq = √klwhere q is the output, k is the firm’s amount of capital equipment and ? is the amount of labour-time employed.(a) In the short run, the amount of capital equipment is fixed at k = 100. The rental rate for k is v = $1, and the wage rate for l is w = $2.Calculate the firm’s short-run average cost (SAC) and short-run marginal cost (SMC) functions. Graph the SAC and the SMC curves for the firm. (b) Where does the SMC curve intersect the SAC curve? Explain why the SMC curve will always intersect the SAC curve at its lowest point.(c) Calculate the long-run total cost of production. For w = $2, v = $1, graph the long-run total cost curve. Show that this is an envelope for the short-run curves computed in part (a).Suppose the long-run production function for a competitive firm is f(x1,x2)= min {x1,2x2}. The cost per unit of the first input is w1 and the cost of the second input is w2. .a. Find the cheapest input bundle, i.e. amount of labor and capital, that yields the given output level of y. .b. Draw the conditional input demand functions for labor and capital in the x1-y and x2- y spaces. .c. Write down the formula and draw the graph of the firm’s total cost function as a function of y, using the conditional input demand functions. What is the relationship between the returns to production scale and the behavior of the total costs? .d. Write down the formula and draw the graph of the average cost function, as a function of y. .e. Write down the formula and draw the graph of the marginal cost function, as a function of y.
