A firm's production function in a market is given by f(2₁, 22) = 2122. Find out this firm's cost function and explain briefly whether or not firms with this kind of production function will be consistent with competitive markets.
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- A firm has a fixed production cost of $4000. For the first 100 units of production, the firm has a marginal cost of $50 per unit produced. Producing more than 100 units has a marginal cost of $70 per unit produced. The firm cannot produce more than 150 units. How much does it cost to produce at q=0? at q=50? at q=100? at q=125? at q=150? Graph the firm’s marginal cost function20.3 (0) A firm uses labor and machines to produce output according to the production function f(L, M) = 4L/2 M/2, where L is the number of units of labor used and M is the number of machines. The cost of labor is $40 per unit and the cost of using a machine is $10. (a) On the graph below, draw an isocost line for this firm, showing com- binations of machines and labor that cost $400 and another isocost line showing combinations that cost $200. What is the slope of these isocost lines?. (b) Suppose that the firm wants to produce its output in the cheapest possible way. Find the number of machines it would use per worker. (Hint: The firm will produce at a point where the slope of the production isoquant equals the slope of the isocost line.) (c) On the graph, sketch the production isoquant corresponding to an output of 40. Calculate the amount of labor and the number that are used to produce 40 units of output in the cheapest possible way, given the above factor prices. Calculate the…1) A firm uses labor and machines to produce output according to the production function f(L,M) = 4L 1/2M1/2 , where L is the number of units of labor used and M is the number of machines. The cost of labor is $40 per unit and the cost of using a machine is $10. a) On a graph, draw an isocost line for this firm, showing com- binations of machines and labor that cost $400 and another isocost line showing combinations that cost $200. What is the slope of these isocost lines? b) Suppose that the firm wants to produce its output in the cheapest possible way. Find the number of machines it would use per worker. (Hint: The firm will produce at a point where the slope of the production isoquant equals the slope of the isocost line.) c) On the graph, sketch the production isoquant corresponding to an output of 40. Calculate the amount of labor and the number of machines that are used to produce 40 units of output in the cheapest possible way, given the above factor prices. Calculate the…
- Given the production function y 1/x05, if Price of output is P and price of input X is V and fixed cost is FC, what is the expression for marginal cost (MC) as a function of Y? O MC = Vy0.5 O MC = -2Vy-3 O MC = Vy-0.5 O MC = y/V1) Miguel and Jake run a paper company. Each week they need to produce 1,000 reams of paper to ship to their customers. The paper plant's long-run production function is: q = 4K L where q is the number of reams produced, Kis the quantity of capital rented, and L is the quantity of labor hired. For this production, MP, = and MP, = The weekly cost function for the paper plant is C= 10K +2L where C is the total weekly cost What ratio of capital to labor minimizes Miguel and Jake's total costs? (Hint: Find the Marginal Rate of Technical Substitution (MRTS) for capital and labor.) b. How much capital and labor will Miguel and Jake need to rent and hire in order to produce 1,000 reams of paper each week? How much will hiring these inputs cost them?If a competitive firm uses two inputs and has the production function F(x1, 22) = Vi + Væ2, then its marginal cost curve is horizontal. O True False
- Suppose that the Acme Gumball Company has a fixed proportions production function that requires it to use two gumball presses and one worker to produce 1,000 gumballs per hour. Graph the average and marginal cost curves for gumballs assuming v = 3, w = 5 Now graph these curves for v = 6, w = 5. Explain why these curves have shifted.Suppose that a production function of a firm is given by q = f(1) = 2√ī. It depends only on labor, whose price per unit is w. The firm is a price taker and the price for the good it produces is p. What is the quantity produced by the firm if the firm maximizes profits and what is the value of profit at that quantity?Miguel and Jake run a paper company. Each week they need to produce 1,000 reams of paper to ship to their customers. The paper plant's long-run production function is: q= 4K^L+ where q is the number of reams produced, K is the quantity of capital rented, and L is the quantity of labor hired. K For this production, MP, =| L and MP, = 34 K K The weekly cost function for the paper plant is C=10K+2L where C is the total weekly cost How much capital and labor will Miguel and Jake need to rent and hire in order to produce 1,000 reams of paper each week, and how much will hiring these inputs cost them?
- 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.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. .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.Trotter Inc is a polling company. Trotter uses both labor, L, (measured in hours worked) and capital, K, (measured in phone lines) to conduct surveys. The production function of Trotter’s is given by Q=10L^0.25 K^0.25 where Q is measured in surveys completed per hour. The price of a unit of L is $16 per hour and the price of a unit of K is $1 per hour. Trotter’s has additional fixed costs of $227 per hour. For parts (a) – (b) below assume that the number of phone lines is fixed in the short run. In particular, Trotter's has 16 phone lines (so K = 16). This results in additional fixed costs in the short run of $16 (ie in addition to the 227). a) In the short run what is Trotter’s (compensated) demand curve for labor? What is the variable cost curve? What is the total cost curve? b) In the short run, what is the marginal cost curve of Trotter’s? What is the average cost curve? What is the optimal size of the firm? Illustrate the short run marginal and average cost curves. For parts (c)-…