Assume there is a linear isoquant where the input combination  K = 10, L = 0 produces Q = 100. Assume that this isoquant has a MRTS (marginal rate of technical substitution) such that an increase in L by 1 unit requires the firm to give up – ½ unit of K. Assume PL= $1 and PK = $1.What is the smallest total cost necessary to produce Q = 100?

A firm has this cost function: C= 1000-4Q+5Q2. The firm is currently producing 3 units of its product. Calculate these a) Total cost b) Average fixed cost c) Total variable cost d) Marginal cost (You must clearly label and type each answer in eCourses, and show your calculations to receive any credit for your answers.)

y= f(x1,x2)=x1ax2b Derive the equation for an isoquant curve.   If a=b=0.5 , the price of factor 1 is 12, and the price of factor 2 is 3, find the cost minimizing input combinations and the total cost of producing 40 units of output.

A firm's short-run cost function is C(q) = 240q – 6g° + 0.6q° + 600. Determine fixed cost, F; average variable cost, AVC; average cost, AC; marginal cost, MC; and average fixed-cost, AFC. The fixed cost function (F) is se F=0 The average variable cost function (AVC) is AVC =- (Properly format your expression using the tools in the palette. Hover over tools to see keyboard shortcuts. E.g., a superscript can be created with the ^ character.) The average cost function (AC) is AC =. (Properly format your expression using the tools in the palette.) The marginal cost function (MC) is MC =. (Properly format your expression using the tools in the palette.) The average fixed cost function (AFC) is AFC = (Properly format your expression using the tools in the palette.) tv 20 MacBook Air DII SO F10 2 F7 FB F9 F2 F3 F4 FS 23 %24 & 3 4 6 8 { [ E Y F G J K > ? х C V N command option .. •- V -

Assume that the situation can be expressed as a linear cost function. Find the cost function. Marginal cost: $225; 140 parts cost $43,000 to produce.

A food truck gyro vendor has weekly fixed costs of ​$550​, and variable costs of $4.55 for each gyro combo prepared.  Let x represent the number of gyro combos prepared and sold each week. Write the weekly cost​ function, C, for the food truck vendor.​ (Hint: The cost function is the sum of fixed and variable​ costs.)

Cost minimization when output is known and total costs are unknown. A factory that you are managing has an hourly production process that can be represented by the following Cobb Douglas Production function: Q = 2K0.50L 0.5 The price of one unit of capital per hour is $20 and the price of one unit of labour per hour is $20. You have been instructed to produce 200 units per hour or Q = 200. Find the optimal amount of labour and capital that you will be using, and compute the total cost.

Suppose that a firm's production function is: q=10L0.50.5 Its marginal product functions are: and MPL = 5K0.5/0.5 = 0.5q/L MPK-5L0.50.5 =0.5q/K. The cost of a unit of labor, w, is $50 and the cost of a unit of capital, r, is $50. Isoquants for output of 140 and 280 are illustrated in the figure to the right. Initially, the firm is producing 140 units of output and has determined that the cost-minimizing quantities of labor and capital are 14 and 14, respectively. Suppose now that the firm wants to increase output to 280 units. If capital is fixed in the short run, how much labor will the firm require? The firm will now require 56.00 units of labor. (Enter your response rounded to two decimal places.) K If the marginal rate of technical substitution is find the optimal level of capital and labor required to produce the 280 units of output. The optimal level of capital is units and the optimal level of labor is ☐ units. (Enter your responses as integers.) K, Units of capital 112 98- 84-…

A firm produces plastic bins using labor (measured in man-hours) and capital (measured in machine-hours), according to the production function Q = f(L,K) = LK, where Q is the number of plastic bins produced. Suppose that the cost of labor is $20 per worker-hour and the cost of capital is $10 per machine-hour. What is the cost minimizing input combination if the firm wants to produce 28,800 plastic bins? Hint: The marginal products are MP, = K and MPg = L.