Suppose MPL = 0.5 ∗ (q/L) and MPK = 0.5 ∗ (q/K). In the long run, the firm will hire equal amounts of capital and labor A) all of the time. B) only when w = r. C) only when w = 0.5 ∗ r. D only when w = 2 * r. E) at no point in time. .
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1) Suppose MPL = 0.5 ∗ (q/L) and MPK = 0.5 ∗ (q/K). In the long run, the firm will hire
equal amounts of capital and labor
A) all of the time.
B) only when w = r.
C) only when w = 0.5 ∗ r.
D only when w = 2 * r.
E) at no point in time. .
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- Suppose, the demand and supply curve in a US manufacturing firm are provided as follows: ES = 20 + 2w ED = 70 − 3w where E is the level of employment and w is the hourly wage. Let’s assume this firm shows the representative wage of the manufacturing industry. Suppose the price of each unit of capital used in this industry is $25. The price of output is constant at $50 per unit. The production function is f(E,K) = E½K ½ , so that the marginal product of labor is MPE = (½)(K/E) ½ If the current capital stock is fixed at 1,600 units, how much labor should the industry employ in the short run? How much profit will the industry earn?A firm uses labour, L and capital K, to produce a single product, X. capital is fixed but labour is variable. The firm’s production function is: X=-0.2L3 + 18L2 + 1620L. Where X is the number of units of the product per week, and L is the number of persons employed. A t what weekly output is marginal cost equal to average variable cost? if the price of the product is $0.20 per unit, what is the maximum weekly wage that the firm would pay rather than close down?A widget manufacturer has a production function of the form q = 6L + 10K . If the wage rate (w) is $4 and the rental rate on capital (r) is $5. Are the returns to scale increasing, constant, or decreasing for this production function? What cost minimization combination of K and L will the manufacturer employs to produce 300 units of output? Suppose that the price of capital increases to $7 per unit. If manufacturer continues to produce 300 units,what cost minimization choice of inputs capital and labor should the firm used. Suppose that the capital input is fixed at K = 3 units in the short run, what is the short run total cost function with q
- Goleta Brewing Company hires only two types of labor, managers and brewing assistants (denoted M and B, respectively). GBC has the following Cobb-Douglas production function F(M,B) = M.5 B.5 and wants to produce 10 barrels of pale ale this week. If the wage of managers is $50 per hour and the wage of brewing assistants is $10 per hour, how many managers and brewing assistants should the firm hire (round to nearest whole number)? How does your answer change when the wage of managers decreases to $30 per hour and the wage of brewing assistants remains constant. Is this result consistent with your intuition?The production function for a firm isq=−0.6L^3+18L^2 K+10Lwhere q is the amount of output, L is the number of labor hours per week, and K is the amount of capital. The wage is w = $100 and the rental rate is r = $800 per time period.a. Using Excel, calculate the total short-run output, q(L), for L = 0, 1, 2, …, 20, given that capital is fixed in the short run and K = 1. Also calculate the average product of labor; APL, and the marginal product of labor, MPL.MPL=−1.8L^2+36L+10 b. For each quantity of labor in (a), calculate the variable cost, VC; the total cost, C; the average variable cost, AVC; the average cost, AC; and the marginal cost, MC. Using excel, draw the AVC, AC, and MC curves in a diagram.A purely competitive firm has a single variable input < (labor), with the wage rate. W0 per period. Its fixed inputs cost the firm a total of F dollars per period. The price of the product is P0. (a) write the production function, revenue function, cost function, and profit function of the firm. (b) what is the first-order condition for profit maximization ? Give this condition an economic interpretation. (c) What economic circumstances would ensure taht profit is maximized rather tahtn minimized?
- The production function for a firm is q=−0.6L^3+18L^2 K+10Lwhere q is the amount of output, L is the number of labor hours per week, and K is the amount of capital. The wage is w = $100 and the rental rate is r = $800 per time period.a. Using Excel, calculate the total short-run output, q(L), for L = 0, 1, 2, …, 20, given that capital is fixed in the short run and K = 1. Also calculate the average product of labor; APL, and the marginal product of labor, MPL. MPL=−1.8L^2+36L+10 b. For each quantity of labor in (a), calculate the variable cost, VC; the total cost, C; the average variable cost, AVC; the average cost, AC; and the marginal cost, MC. Using excel, draw the AVC, AC, and MC curves in a diagram.Given: Q = -0.0250 L3 + 1.5 L2 a) Derive the AP and MP equations (4 pts) b) What is the level of Q where AP and MP of labor is maximum? 2. The chief economist for Lanux Corporation, a large appliance manufacturer, estimated the firm’s short-run cost function for vacuum cleaners using an average variable cost function of the form AVC = a + bQ + cQ2 where AVC = dollars per television and Q = number of vacuum cleaners produced each month. Total fixed cost each month is $180,000. The following results were obtained: DEPENDENT VARIABLE: AVC R-SQUARE F-RATIO P-VALUE ON F OBSERVATIONS: 19 0.7360 39.428 0.0001 PARAMETER STANDARD VARIABLE ESTIMATE ERROR T-RATIO P-VALUE INTERCEPT 191.93 54.65 3.512…Assume that the production function of a firm is Q = L0.23K0.10. L = labor, K = capital.Referring to the information given,i. Calculate the technical suit replacement rate (MRTS) of the firm? ii. Calculate the value and explain the form of return according to the scale (return to scale) of the firmthe?
- The production function for a firm is: q=-0.6L3+18L2K+10L where q is the amount of output, L is the number of labor hours per week, and K is the amount of capital. The wage is w = $100 and the rental rate is r = $800 per time period. a Using Excel, calculate the total short-run output, q(L), for L = 0, 1, 2, …, 20, given that capital is fixed in the short run and K = 1. Also calculate the average product of labor; APL, and the marginal product of labor, MPL. b For each quantity of labor in (a), calculate the variable cost, VC; the total cost, C; the average variable cost, AVC; the average cost , AC; and the marginal cost, MC. Using excel, draw the AVC, AC, and MC curves in a diagram. Hint: you will not be able to solve the total product curve for L as a function of output. So, instead construct a table, See the headings. Use this definition ΔTC/Δq…rofit is found as total revenue (TR) minus total cost (TC). With that in mind, let us now consider the possible profits for the firm that we looked at in assignments 7 and 8, where the firm’s capital is fixed at 2 units and where the cost of capital is $40 per unit per period, while the cost of labor (or wage rate) is $30 per unit of labor per period and the firm has the following short run production function: Labor: 0 1 2 3 4 5 6 7 8 9 Output: 0 6 24 60 120 170 210 240 260 270 Now, let us further assume that the firm is perfectly competitive (i.e., it is a price taker) and that it can sell each unit of the output that it produces for $3 [remember, for price takers, the price (P) is also the marginal revenue (MR)]. (a) Use this information set up a diagram (i.e., an excel chart) that shows total cost (TC) and total Revenue (TR) of the firm per period in the short run with the level of output on the horizontal axis. (b) Also, use…F (L, K) = L0.2K0.7, The wage rate (price per unit of labour) is w = 2 and the capital rental rate (price per unit of capital) is r = 7. Does this production function exhibit increasing, decreasing or constant returns to scale? Explain. What is the marginal productivity of labour and the marginal productivity of capital for (L,K) = (1,1)? Would a firm (which minimises costs) use this combination of labour and capital? Explain. If your answer is yes, then what would be the quantity of production for which the company would use this combination?