Cheburashka uses kiwi fruits (K) and labour (L) to produce juice (q). His production function is: q = min{L/3, K0.5}}, where labour is measured in hours, kiwi fruits in kg, and juice in (large) bottles. For example, if he uses 4 kg of kiwi fruits and 6 hours of labour, he can produce 2 bottles of juice. a) Draw isoquants for q = 1, q=2 and q = 3 on a graph with labour on the horizontal axis and kiwi fruits on the vertical one. b) Let the price of labour-hour be given by w = $18 and the price of fruit by p = $5 per kg. What is the optimal amount of labour and fruit to produce q bottles of juice if Cheburashka strives to minimise costs? (Note that you need to provide expressions L(q) and K(q)). Illustrate on the graph from a) by drawing corresponding isocost lines. c) Draw the Cheburashka's expansion path on a graph from a). Derive an expression for the expansion path, i.e., K as a function of L. How does it depend on the wage and the price of

Cheburashka uses kiwi fruits (K) and labour (L) to produce juice (q). His production function is: q = min{L/3, K0.5}}, where labour is measured in hours, kiwi fruits in kg, and juice in (large) bottles. For example, if he uses 4 kg of kiwi fruits and 6 hours of labour, he can produce 2 bottles of juice. a) Draw isoquants for q = 1, q=2 and q = 3 on a graph with labour on the horizontal axis and kiwi fruits on the vertical one. b) Let the price of labour-hour be given by w = $18 and the price of fruit by p = $5 per kg. What is the optimal amount of labour and fruit to produce q bottles of juice if Cheburashka strives to minimise costs? (Note that you need to provide expressions L(q) and K(q)). Illustrate on the graph from a) by drawing corresponding isocost lines. c) Draw the Cheburashka's expansion path on a graph from a). Derive an expression for the expansion path, i.e., K as a function of L. How does it depend on the wage and the price of

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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1
Suppose a pizza parlor has the following production costs: $3.00 in labor per pizza, $4.00 in ingredients per pizza, $0.40 in electricity per pizza, $3,000 in restaurant rent per month, and $350 in insurance per month. Assume the pizza parlor produces 4,000 pizzas per month. What is the variable cost of production (per month)? The variable cost of production is $. (Enter your response as an integer.)
Which of the following production functions exhibits constant returns to scale (refer to activities and slides ): Group of answer choices q = AL0.5K0.6 q = AL0.3K0.4 q = AL0.5K0.7 Q = 10 L0.3 K0.7
Suppose that a firm’s production function is Q =10 K^(3/4)L^(1/4). The cost of a unit of labor is $1 and the cost of a unit of capital is $3. The manager of this firm is interested in finding the following information: a) Type of returns to scale and the marginal products of labor and capital. b) The marginal rate of technical substitution of labor for capital. Graph the isoquant map. c) The firm is currently producing 100 units of output. Find the optimal cost-minimizing quantities of labor and capital. Graphically illustrate this optimal solution using isoquants and isocost lines. What is the minimum total cost? d) The manager now wants to know the K/L ratio to produce anyoutput level at the minimum total cost. Represent graphically the expansion path in the long run.
Suppose that a firm's production function is Q = F(L) = -1L³-30L² + 5,000L. Its marginal product of labor is MPL = -3L2-60L +5,000. a. At what amount of labor input are the firm's average and marginal product of labor equal (other than at L = 0)? Instructions: Enter your answer as a whole number. units. b. Confirm that the average and marginal product curves satisfy the relationship discussed in the text. When the amount of labor input is less than the quantity identified in your answer above, the marginal product of labor is greater than the average product of labor. When labor is greater than the amount identified above, the marginal product of labor is less than the average product of labor.
1. The following production function is used to produce wheat, q, from capi- tal, K, and labour, L: q = f(K, L) = «³K/3 + B³L/3 a) Describe the role of a and B in this production function. b) Derive the slope of an isoquant for this production function and in- terpret your result. Draw the isoquant in (K L) space, labeling where appropriate. The drawing does not need to be exact, but the curvature needs to be approximately correct. Explain why under- standing the curvature is so important. | c) Does this production function follow the "Law of Diminishing Marginal Returns"? Show your work and explain your answer.
Suppose the production function for widgets is given by: Q = f (K, L) = 2 ∗ KL − K2/2 − L2/2 (a) Suppose L=5 (is fixed), derive an expression for and graph the total product of capital curve (the production function for a fixed level of labor) and the average productivity of capital curve. (b) At what level of capital input does the average productivity reach a maximum? How many widgets are produced at this point? (c) Again, assuming L=5, derive an expression for and graph the MPK curve. At what level of capital input does MPK =0? (d) Does this production function exhibit constant, increasing or decreasing returns to scale?
uppose a Cobb-Douglas Production function is given by the following:P(L,K)=60L^0.8K^0.2where LL is units of labor, KK is units of capital, and P(L,K) is total units that can be produced with this labor/capital combination. Suppose each unit of labor costs $900 and each unit of capital costs $3,600. Further suppose a total of $900,000 is available to be invested in labor and capital (combined).A) How many units of labor and capital should be "purchased" to maximize production subject to your budgetary constraint?Units of labor, LL = Units of capital, KK = B) What is the maximum number of units of production under the given budgetary conditions? (Round your answer to the nearest whole unit.)Max production = units
Consider the production function: Q = L1/4 K 3/4 Does this production show increasing, decreasing, or constant returns to scale? Show your work. I. II. Derive an expression for the marginal product of labor. Ш. Show mathematically whether the marginal product of labor is increasing, decreasing, or constant, as the labor input is increased. IV. Derive the average product of labor. Explain whether the average product of labor is increasing, decreasing, or constant, as the labor input is increased.
plz solve h part.....hand written plzzzzz asap plzzzzzzzzz fast plz asap plzzzzzzzzzzzzzzzz
13. Suppose you have a production technology given by f(x1,x2) = min{2æ1, x2} and you are producing at the point where x1 = 10 and x2 = 20.
13. Suppose you have a production technology given by f(x1,x2) = min{2æ1, x2} and you are producing at the point where x1 = 10 and x2 = 20.