Question1 Imagine you work for a firm that only utilizes labor and capital as inputs and has a CE production function: Where a = 3 = 0.5.y = 2 q=f(L,K) = [aLº + BK²] 1.p = 0.5. a. What is the MPL ? What does this mean economically? b. What is the MPK? What does this mean economically? c. What is the MRTS? What does this mean economically?
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- What is the difference between a fixed input and a variable input?Question2 Imagine that you own a company that is a price taker with the production function: q= = f(L, K) = L0.25 K0.75 a. What is the MPL ? What does this mean economically? b. What is the MPK? What does this mean economically? c. What is the MRTS? What does this mean economically? d. Does this production function have constant, increasing, or decreasing returns to scale? e. What is the short run supply function for the firm? f. What is the derived labor demand for the firm? g. What is the price elasticity of supply? What does this mean economically? h. How does supply shift when the price of labor changes? What does this mean economically? i. What is the price elasticity of labor demand? What does this mean economically? j. How does derived labor demand change when the price of labor changes? What does this mean economically?MCQ 45 Suppose the production function exhibits constant returns to scale, with diminishing marginal productivities for both capital and labour. For this function, we would expect a fall in employment and an increase in the capital stock to generate: A a fall in the marginal product of labour and a fall in the marginal product of capital I do not want to answer this question. a fall in the marginal product of labour, but the change in the marginal product of capital can't be determined from the information provided D a rise in the marginal product of labour and a fall in the marginal product of capital E a rise in the marginal product of labour and a rise in the marginal product of capital F a fall in the marginal product of labour and a rise in the marginal product of capital
- A firm is currently producing such that: MPL = 30 W = 10 MPK = 20 To minimize the cost of production, this firm should: a. Use more labor and less capital which will (likely) decrease the MPL b. Use more labor and less capital which will (likely) increase the MPL C. Use less labor and more capital which will (likely) decrease the MPK Od. Use less labor and more capital which will (likely) increase the MPK v = 201) Suppose the prdduction function for widgets is given by: q= KL – 0.8K² – 0.2L?. a.) Suppose K=10, at what level of labor input does this AP1,reach a maximum and how many widgets are pIdduced at that point? At what level of labor input does MP1=0 and how many widgets are produced at that point? Graph the TP1, AP1 and MP1 curves. b.) Suppose capital inputs were increased to K=20. How would your answers to parts (a) change? c.) Does the widget production function exhibit constant, increasing, or decreasing retums to scale?22. Consider the following production function: Q = 8K³/4L¹/², with capital (K) and labour (L) as the two inputs. (a) Find the marginal products of capital and labour and comment on whether they reflect increasing, constant or decreasing marginal returns. What type of returns to scale does the production function exhibit? (b) What are the average products of capital and labour and what happens to them as inputs increase? How do the marginal and average products relate to each other? Provide an intuitive explanation as to whether this relationship is as you would expect. (c) Assuming that the prices of Labour and Capital are w and r respectively, find the optimal conditional input demands of capital and labour. (d) Suppose that the firm must keep output at the original level, Qo, but that the price of labour, w, falls. By drawing a diagram, illustrate and explain how the firm's optimal inputs would change and what this would mean for the firm's demand curve for labour.
- Question 7 The production function is f(x1, x2) = x¹/²₁x¹/22. 1X a. In the short run the amount of factor 2 (x2) is 100 units. Write down the short run production function and draw a graph of it with output on the vertical axis and the amount of factor 1 on the horizontal axis. b. How does the marginal product of x1 in the graph you drew in a) change with the amount of x₁? Discuss what you observed in the graph that helped you to determine your answer. Write out the equation for an iso-profit line and add it to the graph you drew in part (a). Show how you derive the iso-profit line from a profit function that depends on output (y) and the amount of the inputs (x1 and x2). d. If the price of factor 1 is $10, the price of factor 2 is $15, and the price of output is $20, what is the short run profit maximizing choice of x₁? (The marginal product of factor 1 is 5 1/2 You will need to use this information to solve for the answer to c.) How did you know that this was the answer? Use the…Question 2: Consider the following production function that depends only on labor:Q = 2L+6L² - 3L³ 1. Compute the APL (average product of labor). 2. Compute the MPL (marginal product of labor). 3. What is the value of L* at which APL is the highest? 4. For L > L*, which one is bigger, APL or MPL? How about when I < L* and L = L* ? 5. Draw APL and MPL on the y-axis as a function of L on the x-axis. Label the point of the intersection of APL and MPL.5. Suppose the production function is given by f(E, K) = E'/³K²/3. The hourly wage rate is $2 and the price for a unit of capital is $32. The output level is ĝ = 144 and the price of the output is $30. (a) Write a firm's CMIN problem. (b) Impose FONC to find MP(E) = w and MP(K) = r. %3D
- Consider the following production function: q = 32LK + 10L2 - Assume capital is fixed at K= 25. At what level of employment does the marginal product of labor equal zero? The marginal product of labor equals zero when (Enter a numeric response using an integer.) Beyond a labor input of 40, the marginal product of labor is 20 étv MacBook Air DI DD F3 F5 F6 F7 FB F10 FW 2# $ & 3 4 5 8 9 E R Y P D F G н J K C V B N M command V5. A company that produces auto parts has a production function of Q = 300 L-75 K-5. %3D If L= 250 and K= 25, what is the output of auto parts? If L increases to 350, what is the output of auto parts? What does the change in output show regarding labor as a factor of production?Question1 Imagine you own a firm with the production function q=f(L,K) = Lº.2 K0.8 a. What is the MPL ? What does this mean economically? b. What is the MPK ? What does this mean economically? c. What is the MRTS? What does this mean economically? d. Does this production function have constant, increasing, or decreasing returns to scale?