Question2 Imagine you work for a firm that only utilizes labor and capital as inputs and has a CES production function: q = f(L, K) = [aLº + BK²] Where a = B=0.5.y = 1.p = 2. 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 CES function have constant, increasing, or decreasing returns to scale?
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- 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 capitalA 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 = 20
- 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. %3DIn the production process, both the average product and marginal product of the variable input rise first, then fall, and then rise to infinity OFalse O True 27 WQuestion1 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?
- 5. 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?Be the production function Q (K, L) - : (K} +213), that depends on the quantitiess Used from inputs Kand L; and be the point (K, L) = (1,2). (a) What is the effect on the production of an increase of a unit in the amount used of INPUT L, L, Other things being equal?? (b) What is the effect on the production of an increase of 1% in the amount used of INPUT L, Ceteris paribus?3. Imagine we live in a classical world. Suppose that the production function is Y = L²K², where L is the amount of labor and K is the amount of capital. The economy has 100 units of labor and 100 units of capital. a. Does the production function show Constant Returns to Scale? Why? b. Derive an expression for the marginal product of labor. Is the marginal product of labor diminishing? How does an increase in the amount of capital affect the marginal product of labor? Explain. What are the real wage and rental price of capital? d. What is the income share paid to labor? What is the income share paid to capital? C.
- 2-lf you have the following production function Q=f( L,K), answer the following : 1. is this function tong or short run? 2. Draw TP! , MPL, APL. 3. Show the stages of the production. 4. Expiain the reiationship between iviPi & APL. 5. When MPL=0, what does that mean ?Output per worker (S, thousands) Production lunction (after 225 technological progre Production function 15 20 30 Capital equipment per worker (S, thousands) The figure shows an economy's production function before and after a technological progress. Based on this information, which of the following statements is correct? O The average product of capital at Ais 250,000/70,000 -3.57 O The marginal product of capital atA is (85.000 - 70.000)/ (300,000 - 250,000) = 0.30 O The particular shape of the production function indicates diminishing marginal product of capital As a result of a technological progress, the marginal product of capital rises but the average product of capital remains constant for a given level of capital per workerD Question 32 BBT produces 137.5 units daily. The productivity factor of BBT's production is 2.75 and has elasticities of capital and labor of 0.4 and 0.6, respectively. In addition, the capital input used in its production is 55, 137.5, 275, and 343.75. How much is the labor input if the capital input to produce these units is 137.5? Round your answer to one decimal place.