A farmer producing two commodities has a profit function:П(91,92) = -50+4q1-2q+3q2 - 92 - 9192where q₁ and q₂ are the output levels of commodity 1 and 2 respectively. The cultivationof the two commodities uses a K unit of scarce resource. The farmer's constraint thatinvolves the use of this scarce resource is given by:K = 91 +292Solve the optimal level of q₁ and q2. (Hint: the answer will be in functions of K.)

Step 1:To solve for the optimal level of q1 and q2 in terms of the scarce resources K, we will use…

Answered: A farmer producing two commodities has…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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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 =…
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Consider a country that produces computers (C) and food (F) using capital (K) and labor (L). Both industries are perfectly competitive. The factors of production are complements. As a result, unit factor requirements are fixed and given by: aKc = 3, aKF=1, aLc = 2 and aLF = 4. Suppose that this economy has 100 units of capital and 150 workers. (c) Suppose that the world price of computers is $16 and the world price of food is $12. Assume that the Home country produces both goods. What are the free trade factor price levels W and R? (d) How many computers and units of food will the economy produce? (e) Suppose that the endowment of labor increased to 200. Compute the new equilibrium wage, rental rates and quantities produced in the new equilibrium. Provide the intuition of your results.
A food manufacturer is trying to maximize profit by selling wheat-based cereal (C) and wheat bread(B) with raw wheat (W). The production functions are: Cereal: C = 30WC – 1.5WC2 Bread: B = 63WB – 2WB2 Constraint: WC + WB = 9,820 Profit is $1.00 per box of cereal and $0.50 per pack of wheat bread. There are 9,820 units of raw wheat available. How much wheat should go to the cereal (WC)? Enter as a value. ROUND TO THE NEAREST WHOLE NUMBER.
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Let a firm's production function be f(K, L) = min{2K, L}. a) Solve for the contingent demand functions for K and L.
Problem 3: Long-Run Cost minimization Consider two cost-minimizing firms producing drones as their single output. Firm 1 produces traditionally, using capital K and labor L as inputs. Firm 2 has a close relationship with an artificial-intelligence research laboratory and may also use androids A as an input.The input prices are r > 0 for capital, w > 0 for labor, and a > 0 for androids.The firms’ production functions are as follows: F1 (K, L)=5KLF2 (K, L)=(L + 2A)4K Question: A customer orders exactly ¯q = 2000 drones from each firm. Describe each firm’s cost-minimization problem in formal terms
A firm faces the production function O = 6K L05. If it can buy input K at £32 a unit and input L at £8 a unit, what combination of L and K should it use to maximize production if it is constrained by a fixed budget of £36,000?
Road Runner Co is a Pakistani manufacturer making Bicycles. It exports to two markets,Bangladesh and Sri Lanka. Demand for Bicycles in thesetwo markets is given by the following Functions: Bangladesh Q1 = 12 – P1 Sri Lanka Q2 = 8 – P2 Where Q1 and Q2 are respective quantities sold (in thousands) andP1 and P2 are the respective prices (in Pak. Rupees per unit) in the two markets. Total cost function is C = 5 + 2 (Q1+ Q2) (i) Company is effectively able to price discriminate in the two markets. What will be the total profits? (ii) Suppose the company does not engage in price discrimination. By charging the same price in the two markets what are the profit maximizing levels of price, output, and the total profits? (iii) Analyze, with graphs, the two alternative pricing strategies available to the company.
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