1. Juan Valdez owns a coffee farm in Colombia. His production function is:f (x1, x2) = (x1 – 1)0.25 x9-5.Assume the price of input 1 is r and the price of input 2 is w..(a) Write down an expression for the technical rate of substitution.(b) Find Juan's demand for inputs conditional on the quantity y of coffee Juanwants to produce.(c) Find Juan's cost function.(d) What is the supply function of Juan's firm?2. Show that the profit function is convex in (p, w).3. Find the profit function for the Cobb-Douglas production function f(¤1, 12) = Ax†' x"with A > 0, a1, ¤2 > 0 and a1 + a2 < 1.4. Verify Hotelling's Lemma for the Cobb-Douglas production function with a1+a2 < 1.5. Find the supply function and the input demand functions for the CES productionfunction:f(r1, F2) = A(ax{ + (1 – a)x2)8/e,%3Dwhere A > 0, B > 0, 0 < a < 1, and 0 + p< 1.6. Find the profit function for the CES production function.7. Verify Hotelling's Lemma for the CES production function with B < 1.

y = (x1 - 1)0.25x20.5 (a) MP1 = y/x1 = [0.25x20.5] / [(x1 - 1)0.75] MP2 = y/x2 = [0.5(x1 - 1)0.25]…

Answered: Juan Valdez owns a coffee farm in…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Consider the input output table below Table (Inter) final Total (Agric) (Manuf) (Mining)demand (Inter) Agric 106 47 180 898 1231 Manuf 75 32 80 1167 1354 Mining 31 115 100 977 1223 PrimaryLabour 949 760 363 Capital 70 400 500 where: (Agric = Agriculture),( Manuf = Manufacturing),(Inter = !3! %3D Intermediate) A. Calculate the input coefficients and fill in the appropriate spaces in the table below. Use four (4) decimal places. Agric (Manuf) (Mining) Agric Manuf Mining Labour Capital
X If total revenue received from the sale of x items is given by R(x) = 10 In (4x + 1), while the total cost to produce x items is C(x) = ¹ (a) The marginal revenue (b) The profit function P(x) (c) The marginal profit when x = 40 (d) Interpret the results of part (c). (a) How can the marginal revenue be found? A. Find R(x) - C(x). B. Find the derivative of R(x). C. Find the derivative of R(x) - C(x). R( 2 ). D. Find R find the following.
2. If c=3q-3q2+q3is a cost function, when is marginal cost decreasing?
Find the average cost function for each firm
4) A firm faces a production function of twittle-twaps: Q(K,Lp,Ln) = 5*K(2/5)*LP(1/3)*LN(1/5) per hour, where capital (K), production labor (LP), and non-production labor (LN) are input factors used in production. The firm operates in a competitive market, where they are a price taker within the capital & labor markets and its own price (r = 40, wP = 25, wN = 50, P = 20). Answer the following.a. If capital and non-production labor are fixed at K = 32 and LN = 243, what is the general form MPLP and graph Q wrt to LP changing [you do not need to solve for LP yet].b. Is this production function decreasing, constant, or increasing returns to scale and why.c. Given the wage of production workers and the price of twittle-twaps, what is the optimal number of LP to employ to maximize profits and the quantity produced (VMPLP = wP).d. If the firm can control both K and LP, what does the Isoquant curve look like and its slope in relative terms if LN is fixed at 243 units [IQ slope =…
the wage rate of labour is GH¢2 per hour and capital is rented at GH¢5 per hour. Also, the unit price of chocolate pellets is GH¢0.75 and total cost of production is GH¢1,000. Suppose the firm’s production function (Q) follows a Cobb-Douglas specification given as:? = 14?0.5?0.5 + 10
6 A production function is given by f(x1,x2)=(max{x1,x2})^0.5. Prices of inputs are p1=10 and p2=20. What is the lowest cost of producing 10 units of output?
2 The company Shirts Galore has figured its total cost of producing and sclling x units of T-shirts per month is given by the equation C(x) = 120 +2.5x-0.0002r. a) Write a rational function to represent the average cost of producing and selling a shirt. b) If the production level is 1200 shirts per month, find the average cost of producing and selling a shirt. c) If the shirts are sold for $7.98 a shirt, what is the profit realized on producing and selling 1200 shirts per month? d) What price must be charged when selling the shirts for a profit of $7368 to bc made on 1200 shirts in one month? * A large company is considering changing
25) If a firm has the cost function C(q) = 5q² + 20q + 180 and the marginal cost function MC(q) = 10q + 20, at what quantity is its average cost minimized?
Suppose that the total cost (in dollars) for a product is given by C(x)=1300+ 160 In(2x + 1) where x is the number of units produced. (a) Find the marginal cost MC function. MC = (b) Find the marginal cost when 160 units are produced. (Round your answer to the nearest cent.) $ Interpret your result. The profit from the next unit will be approximately this amount. This is the total cost of producing 160 units. ◇ This is the total profit from producing 160 units. ○ It will cost approximately this amount to make the next unit. (c) Total cost functions always increase because producing more items costs more. What then must be true of the marginal cost function? ○ MC ≥ 0 ○ MC > 0 ○ MC ≤ 0 ○ MC = 0 ○ MC <0 Does it apply in this problem? ○ Yes Ο ΝΟ
X and X2 are the two factors used in production A firm's production function: fcx₁, x₂) = max {x₁, X₂} the price of X, is W₁=8, and the price of X₂ is W₂=10 The firm paproduce 100 total units of output, what is the total cost?
Law of diminishing returns......

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