Homework Answers
Production function is a function of labor only so optimal quantity of labor hired will be the one where marginal product of labor is equal to real wage
MPL = w/p
2*0.5*(L)^-0.5 = 40/160
L^-0.5 = 0.25
This gives optimal value of L = 0.25^(-1/0.5) = 16.
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Single Variable Optimization
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2. A firm produces (= units of a commodity when labour input is L units. The price obtained per unit of output is P, and the price per unit of labour is w, both positive. (a) Write down the profit function w. What choice of labour input L=L* maximizes profits? (b) Consider L* as a function L (P, w) of the two prices, and define the value function (P, w) = (L* (P, w), P, w) Verify that ax/aP =...
5. (a) (5 points) A firm produces aln(L 1) units of a commodity when labour input...
5. (a) (5 points) A firm produces aln(L 1) units of a commodity when labour input is L units The price obtained per unit is P and price per unit of labour is w, both positive, and with w<aP. Write down the profit function π. What choice of labour input L = L* maximizes profits? (5 points) Consider L* as a function of all the three parameters, L*(Ru, a), and define π"(Pu, a)= r(L', P w, a). Verify that a./...
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Exercise 2. A Los Angeles firm uses a single input (labor) to produce a recreational commodity according to a production function Q(L)4VL, where L is the amount of labor it uses. The commodity sells for $100 per unit. The input costs $50 per unit. Write down a function that states the firm's profit as a function of the amount of input. b. What is the profit-maximizing amount of input? What is the profit- maximizing amount of output? How much profit...
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(1 point) A company produces x units of commodity A and y units of commodity B each hour. The company can sell all of its units when commodity A sels for p-100-8x dollars per unit and commodity B sells for q = 40-10y dollars per unit. The cost (in dollars) of producing these units is given by the joint-cost function C(x, y)-5xy +5. How much of commodity A and commodity B should be sold in order to maximize profit? Commodity...
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- Julia operates a cost-minimizing firm that produces a single output using labor (L) and capital...
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A perfectly competitive firm uses a single input (labor) to produce a good according to a...
A perfectly competitive firm uses a single input (labor) to produce a good according to a production function Q(L) = 2/7 , where Lis the amount of labor it uses. The good sells for $180 per unit (price). The input costs $15 per unit (wage). 1. (20 pts) What is the profit-maximizing amount of input (L)? 2. (10 pts) What is the profit-maximizing amount of output (Q)? 3. (10 pts) How much profit does the firm make when it maximizes...
2. A firm produces two different kinds, A and B, of a commodity. The daily cost...
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Name: 1. Consider a firm that hires workers (L) and produces output (Q). a. If the...
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Exercise 2. A Los Angeles firm uses a single input (labor) to produce a recreational commodity according to a production function Q(L)4VL, where L is the amount of labor it uses. The commodity sells for $100 per unit. The input costs $50 per unit. Write down a function that states the firm's profit as a function of the amount of input. b. What is the profit-maximizing amount of input? What is the profit- maximizing amount of output? How much profit...
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2. (3 points) A company produces x units of commodity A and y units of commodity B. All the units can be sold for p = 90 – x dollars per unit of A and q = 60 – y dollars per unit of B. The cost (in dollars) of producing these units is given by the joint-cost function C(x, y) = + 2xy + y? What should x and y be to maximize profit? What is this maximum profit...
- Julia operates a cost-minimizing firm that produces a single output using labor (L) and capital (K). The firm's production function is Q f(L, K) = min{L, K}}. The per-unit price of labor is w = 1 and the per-unit price of capital is r = 1. Recently, the government imposed a tax on Julia's firm: For each unit of labor that Julia employs, she must pay a tax of £t to the government. (a) Graph the Q unit of...
A perfectly competitive firm uses a single input (labor) to produce a good according to a production function Q(L) = 2/7 , where Lis the amount of labor it uses. The good sells for $180 per unit (price). The input costs $15 per unit (wage). 1. (20 pts) What is the profit-maximizing amount of input (L)? 2. (10 pts) What is the profit-maximizing amount of output (Q)? 3. (10 pts) How much profit does the firm make when it maximizes...
2. A firm produces two different kinds, A and B, of a commodity. The daily cost of producing x units of A and y units of Bis C(x,y)=2x² - 4xy + 4y2 - 40x - 20y + 514 Suppose that the firm sells all its output at a price per unit of $24 for A and $12 for B. (a) Find the daily production levels x and y that maximize profit. (b) The firm is required to produce exactly 54...
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