Practice multiple choice MT II - with answers

Problem 1 a) The local cleaner launders white clothes using the production function q = 3B + G, where B is the number of cups of a brand bleach and G is the number of cups of a generic bleach that is half as potent. a.1) In a graph, draw an isoquant. a.2) What are the marginal product of B and G? What is the marginal rate of technical substitution? Technology

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 Juan wants 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 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.

24. A specific production process can be represented by the production function, f(x1, x2) = (x 1/2 + x 1/3) 3. A. How much x₁ could the firm give up if it wanted to use 1 extra unit of x2 and still wanted to produce an identical level of output? B. Labeling everything and being precise, draw the isoquant corresponding to q = 4. = 9. C. On the same graph, draw the isoquant corresponding to q D. Between the isoquants you just drew, does the production technology display decreasing, increasing, or constant returns to scale? E. Analytically determine whether the production process has global returns to scale that match your local results from part D. Recall that in order to claim global returns to scale, your result must hold for ALL possible values of x1 and x2.

Juan Valdez owns a coffee farm in Colombia. His production function is:  f(x1​,x2​)=(x1​−1)^0.25 x2^0.5​   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 Juan wants to produce. (c)  Find Juan's cost function. (d)  What is the supply function of Juan's firm?

6. Duane breeds parrots for a living. He has discovered that the production function for parrot chicks (Q) is: Q = K2 L12 where K is capital (for example nest boxes, cages and the like) and L is parrot food. The price of K is $8 and the price of L is $2. a. What type of production function is this? b. Does this production function exhibit constant, increasing or decreasing returns to scale? Explain. c. What is the average product of capital?

For each of the following cases, determine whether the firm should (A) Use more labor and less capital, or (B) Use more capital and less labor. 1. The marginal rate of technical substitution is 2 (i.e., the marginal product of labor is twice the marginal product of capital) and the input price ratio is 3 (i.e., a unit of labor costs three times as much as a unit of capital) 2. The marginal rate of technical substitution is 2 (i.e., the marginal product of labor is twice the marginal product of capital) and the input price ratio is 1 (i.e., a unit of labor costs the same as a unit of capital) 3. The marginal rate of technical substitution is initially equal to the input price ratio, but the firm's machines depreciate, so that the marginal product of capital decreases. 4. The marginal rate of technical substitution is initially equal to the input price ratio, but the firm successfully negotiates a lower rate of rent for their machines, so that the price of capital decreases. 5. The…

Question 4 The firm can use two inputs, L and K. The price of L= 20 and price of K = 30. Total cost = 300. As usual in the two input graph, units of L are on the horizontal axis and K on the vertical. The slope of the isocost line is [Select] The maximum units of K that can be purchased is [Select] The maximum units of L that can be purchased is [Select] 2 pts Is the bundle of K-9 and L- 5 on the isocost line? [Select]

which of the following best describes marginal product?A.)Left over output- the loaves a bakery makes but does not sell that goes unused. B.) The total number of loaves a bakery can create with 5 workers and a fixed amount of capital. C.) The loaves made by a bakery using a substandard quality flour that ultimately harms business profits. D.) When the number of bakery staff increases from 2 to 3 bakers, 5 additional loaves are made.

Suppose that a firm’s production function is  q =10L0.5K0.5  (i.e. q = 10√L√K). The cost of a unit of labour is €20 and the cost of a unit of capital is €80.  The firm wants to produce 80 units of output. The marginal rate of technical substitution is K/L The optimal level of labour required to produce 80 units of output is      A. 16   B. 8   C. 4   D. 2

3. Duane breeds parrots for a living. He has discovered that the production function for parrot chicks (Q) is: Q=K0.5 p0.5 where K is capital (for example nest boxes, cages and the like) and F is parrot food. The price of K is $8 and the price of F is $2. (b) Does this production function exhibit constant, increasing or decreasing returns to scale? Provide a graph of the function using Excel.

Isoquant curves and isocost curves are tools that can explain how a firm might best respond to changes in the production environment.  Present an example of an isocost curve where labor and capital are the two inputs, and explain what it is using language someone not trained in economics could understand.  Present an example of an isoquant in the same diagram you used for your isocost curve, and draw the isoquant so it cuts the isocost curve twice. Explain what an isoquant is using language someone not trained in economics could understand.  Label the two points A and B, where the isocost and isoquant curves intersect.  Present a logical argument that explains why the firm should operate neither at point A nor point B, and present a point that would be optimal by drawing a new isoquant curve in the diagram.  Add a second isocost curve to your diagram such that the firm is spending more money on inputs.  Add a third isoquant to your diagram to show a firm that would become more capital…

I have graphed the isoquant line but I can’t figure out how to graph the isocost line? Could you verify my math and show the isoquant and isocost line graphed please?

Suppose pigs (P) can be fed corn-based feed (C) or soybean-based feed (S) such that the production function is P=2C+5S. If the price of corn feed is $4 and corn feed is on the horizontal axis, and the price of soybean feed is $5 and soybean feed lies on the vertical axis, what is expansion path? the horizontal axis Oa. Ob. Oc. S=2C/5 C. d. C=5S/2 the vertical axis

Suppose that a firm’s production function is  q =10L0.5K0.5  (i.e. q = 10√L√K). The cost of a unit of labour is €20 and the cost of a unit of capital is €80.  The firm wants to produce 80 units of output. The marginal rate of technical substitution is K/L The optimal level of capital required to produce 80 units of output is    A. 16   B. 8   C. 4   D. 2

sub= 24 help

3. Duane breeds parrots for a living. He has discovered that the production function for parrot chicks (Q) is: Q=K0.5 p0.5 where K is capital (for example nest boxes, cages and the like) and F is parrot food. The price of K is $8 and the price of F is $2. (a) What type of production function is this? Explain. (b) Does this production function exhibit constant, increasing or decreasing returns to scale? Provide a graph of the function using Excel. (c) Find the marginal products of capital and food. (d) Suppose that Duane wants 144 parrot chicks, how much K and F should be employed to minimise costs. What is the cost of producing 144 parrot chicks? 1 1 (e) Suppose that Duane is faced with the same problem as in (e) except that he has a fixed amount of K. In fact, K = 16. How much F should be bought to minimise costs? What is the total cost?

a.)Suppose that labor is the only variable input in the production process. If the marginal cost of production is diminishing as more units of output are produced, what can you say about the marginal product of labor?b.)What are economies of scale? What are economies of scope? What is the difference between the two?

.2. Tiva has a crafts store that makes jewelry using beads (B) and copper (C). Her productionfunction for jewelry is given byQ = B0.4C0.4Suppose she can buy beads and copper at prices PB and PC, respectively.(a) Calculate Tiva’s marginal rate of technical substitution between B and C.(b) Does this production function have increasing, constant, or decreasing returns to scale?Explain. (c) Set up the cost minimization problem you would use to calculate Tiva’s cost functionC(Q) in Lagrangian form. (Note: You do not need to solve it or derive first orderconditions.Suppose Tiva decides to branch out in her jewelry offerings by getting a 3D printer. The costof producing new 3D printed jewelry isC(Q) = 25 + Q24For the rest of this problem, assume Tiva can produce fractions of jewelry, don’t worry aboutrestricting your answers to whole numbers.(d) Compute Tiva’s marginal cost and average cost of production for 3d printed jewelry.(e) Explain why she will shut down when the market price falls…

The figure shows the production function of a farmer who produces grain by working certain hours each day.     Which of the following statements is correct about this production function?         a. The slope of the production function represents the marginal rate of substitution. b. The ceteris paribus assumption means that the farmer becomes more productive as he works more hours. c. A rightward movement from B along the production function implies that the farmer has better technology. d. This production function exhibits economies of scale. e. A technological improvement would shift up the production function

Q2 solution needed

We know there is a link between productivity and costs. For example, recall the link between the marginal physical product of the variable input and marginal cost. With this in mind, what link might there be between productivity and prices?

Lesson 7- Production Question 1

There are two factors of production, X and Y. They are being used to produce a fixed amount of output called A. If the amount of output, A is held constant, and the isoquants are convex, would the price of X going down always mean less of Y is used? Explain why or why not by explaining through the use of a graph.

Joe owns a small coffee shop. His production function is q = 2K0.5 L where q is the number of cups of coffee produces, K is the number of coffee machines, and L is the number of employees. a) If K=1 and L=2, the marginal rate of technical substitution is _________. b) If, starting from 1 machine and 2 employees, Joe hires one more employee, then he can produce the same quantity of cups of coffee with  _________ less machines.