b Now suppose Q = 2L +3K. Let the market price of L be w = 5 and the price of K be r = 4. Let both L andK can vary with production. Compute the input demand functions as a function of Q. (4 Points)c Calculate the marginal cost and average cost of the above function in subpart (b). Show them graphically. Atwhat prices of textile will the producer shut down production. (3 Points)d Now suppose Q=10LK. The market prices of inputs are as in subpart (b) above. Compute the inputdemand functions as a function of Q. Find the optimal production when the price of textile is $10 per yarn.(5 Points)

b) Suppose the production function is Q = 2L + 3K, where Q represents the output quantity, L is the…

Answered: b Now suppose Q = 2L +3K. Let the…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Craig and Javad run a paper company. Each week they need to produce 1,000 reams of paper to ship to their customers. The paper plant's longrun production function is Q = 4KL, where Q is the number of reams produced, K is the quantity of capital rented, and L is the quantity of labor hired. The weekly cost function for the paper plant is C = 20K + 4L, where C is the total weekly cost. (a) What ratio of capital to labor minimizes Craig and Javad's total costs? (b) How much capital and labor will Craig and Javad need to rent and hire in order to produce 1,000 reams of paper each week? (c) How much will hiring these inputs cost them?
A5
1/3 1/3 Assume y = f(x1, x2) = x1 x2 . If the input prices are w₁ and w₂ what is profit maximizing y level of output? What is the profit?
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The cost function of producing Q units of good: C(Q) = 4Q2 + 16Q + 40 Write down the average cost and marginal cost. Find the value of Q whichminimizes average cost? (Show necessary and sufficient conditons)
A firm’s production is represented by the following function: Q = L1/4 K3/4 . The rental rate of capital (r) is $40 and the wage rate (w) is $12.a. For a given level of output, what should be the ratio of capital to labor in order to minimize costs?b. How much capital and labor should be used to produce 400 units of output? What is the total cost?c. What is the short run total cost if output is decreased to 300 units?d. How would the capital labor choice and total cost change in the long run?e. Would the firm prefer to relocate if input prices are r = 60 and w = 8 at an alternativelocation assuming relocation is costless?
A perfectly competitive rm produces output q with capital K and labor L according to the production function: q = f(K, L) = 4K 1 4L 1 4 The price of labor is w = 4, and the price of capital is r = 4. The rm has xed costs equal to 8. The current market price is 8. (a) Prove that this production function has decreasing returns to scale. (b) Find the optimal (cost-minimizing) ratio of capital to labor inputs K L for any level of output (use scale expansion path). (c) For any q, nd the cost minimizing inputs as functions of output: i.e., derive functions L(q) and K(q).
1. Suppose the total-cost function for a firm is given by C = qw 1/4 3/4 a. Use Shephard's lemma to compute the (constant output) demand functions for each input, k and 1. b. Calculate the average cost and marginal cost. c. Describe the returns to scale for the underlying production function for q.
In a fishery the long-run harvest function (harvest volume) is H(E) = aE – bE², with a, b representing positive constants and E is fishing effort. - Total cost is TC(E)= cE,with c being the unit cost of effort. Total revenue is TR(E) = pH(E), with p being the constant price of fish. Suppose that, because of an increase in world demand, the price of the fish from this fishery rises significantly. • Illustrate and explain the impact of this price-increase on the fish stock and the competitive level of effort (or employment) in the fishery. What can be said about the long-run impact on the fish catch? Is it positive, negative, or indeterminate? Explain.
Question 2: This question refers to a firm's production and profit maximization in the long-run. The firm's cost function is: TC = 20E + 100K. 2.a) In the graph below, plot the firm's isocost line representing total costs of $120,000. Indicate on the figure the value of the isocost's slope. Also indicate where the isocost line intersects with the horizontal and the vertical axes. K E 2.b) The firm is considering producing a total of 200 units. If the firm wants to minimize the cost of producing this level of output, what must the marginal rate of technical substitution be?
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Problem 5 Suppose that a firm has a production function f(K, L) = 12L¹/3 K¹/3 and that w and r are input prices and p is output price. The firm does not change those prices. a) Show that the firm's profit π is a concave function of (K, L). b) Find (K*, L*) that maximizes the profit, as a function of (w,r, p).

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