) What is the equation of the long-run aggregate supply curve? The income velocity of money is constant, and the money supply is fixed: V = 0.15 M = 5600 The production function is Y = F(L, K) = 8 x √L x √K The endowment of resources is given by the input combination (L, K) = (49, 25)
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) What is the equation of the long-run
The income velocity of money is constant, and the money supply is fixed:
V = 0.15
M = 5600
The production function is
Y = F(L, K) = 8 x √L x √K
The endowment of resources is given by the input combination
(L, K) = (49, 25)
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- Answer 1. A new coal-fired power plant will increase aggregate production.Which element of the aggregate production function Y = A × F(K, H) willthis power plant increase?A) AB) FC) KD) HConsider the following variation of the aggregate production function. Now firms must use oil M to produce output (in addition to labor and capital). The price of a unit of oil is p П max II = AK°L³M – wL-rK – pM (a) Find a first-order condition for the firm's demand for oil. (b) What must be true about the parameters a, B, and y if this production function exhibits constant returns to scale? (c) If the price of oil p rises, what would you expect to happen to carbon intensity (the ratio of oil per unit output: M/Y) in this economy? What happens to the revenue share of oil (the ratio of total oil payments to output: pM/Y)?A firm faces the following production function, Y = AKa L¹-a (1) Here Y is output, K is capital, L is fixed labour, and A is a measure of technology. The firm uses an optimal amount of capital determined by the condition, (2) MPK = r + 8 Where MPK is the marginal productivity of capital, r is the real interest rate, and Ổ is the depreciation rate. Suppose that a = 0.5, L = 25, and A = 20. Further, the real interest rate, r, is 2% and capital depreciates at a rate (8) of 18% per year. What is the optimal amount of capital this firm should install? [2 marks] Now suppose that A increases to 25, while a, L and & remain unchanged. Further, the optimal capital stock remains at the amount you found in part (c). What does this mean must have happened to the real interest rate? Find the new real interest rate and draw a clear diagram showing MPK and user cost of capital lines before and after the changes to A and r. [4 marks]
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- 1. A new coal-fired power plant will increase aggregate production.Which element of the aggregate production function Y = A × F(K, H) willthis power plant increase?A) AB) FC) KD) HFor the production function Q = K0.7L0.6 and the budget 122 = 4K + 4L find the NEW LEVEL of the cost (budget) for the new optimal employment of capital (K) and labor (L) in the long run after output has change by a factor of 2.0. Please enter your response as a positive number with 1 decimal and 5/4 rounding (e.g. 1.15 = 1.2, 1.14 = 1.1).A U.S. electronics firm is considering moving its production abroad. Its production function is: q=L = L 0.50 0.50 (based on Hsieh, 1995), so MPL = 0.5q/L and MPK = 0.5q/K. In the United States, w=$10=r. At its Asian plant, the firm will pay a 10% lower wage and a 10% higher cost of capital: w* = $9.09 and r* = $11.00. What are L and K and what is the cost of producing q= 100 units in both countries? (for all responses, enter a real number rounded to two decimal places) In the U.S., L is 100, K is 100, and the cost of production is $ 2000 In Asia, Lis
- A producer has the following technology.y= 6K^(1/2)L^(1/2) a) Prove formally that the production function exhibits constant returns to scale (use “λ” argument). b) Find analytically MPL and MPK. Is MPL increasing, decreasing, or constant inL? Is MPK increasing, decreasing, or constant in K? c) Short-run: Given stock of capital ̄K= 1 find labor demand (formula) of a competitive firm. Find equilibrium real wage rate if labor supply is given by Ls= 9 (one number). d) Assume again ̄K= 1 and that Ls= 9. The government adopts a real minimum wage of wmin/p=(3/2). Find labor demand (one number) and the unemployment rate (one number). Please depict the equilibrium on a graph with the real wage on the vertical axis and labor on the horizontal axis, indicating the equilibrium quantity of labor, wage, and unemployment, as well as the relevant curves. e) Find the cost function given prices of inputs wK= 4 and wL= 1 (formula). Plot the cost function on a graph, indicating the slope of the cost…Consider an economy that produces goods and services according to the production function F (L, K) = 90L Ki,where L represents the number of workers in an economy and K represents the combined units of physical and human capital. The marginal products of labour and capital are: (登) MPL = 60 30(£) MPK = Question 1 Initially: there are 27 workers and 64 units of capital. Part (a): What is the economy's real GDP and GDP per capita? 1st scenario Suppose L increases to 125 while capital remains constant at 64: Part (b): Calculate the economy's real GDP and GDP per capita. Part (c): Relative to the initial scenario (L = 27 and K = 64), how much did MPL change by? 2nd scenario Now suppose L remained constant at 27 workers and capital increased to 216 units: Part (d): Calculate the economy's real GDP and GDP per capita. Part (e): Relative to the initial scenario (L = 27 and K = 64), how much did MPK change by? 3rd scenario Finally, suppose L = 54 and K = 128. Part (f): Calculate the economy's…Suppose that the production function for the economy is given by: Y = AL/3K/3 Suppose that this economy has 1,000 units of Labour, and 125 units of capital, and TFP (A) is equal to 10. The Short-Run Aggregate Supply Curve (AS) here is given by: Y = 5p And when we consider the AEF at a price level of $1,400, the main components of it (C, I, & G) are given by (we are assuming a closed economy NX = 0): C = 300 + 0.8Y I = 300 G = 200 1. What is potential GDP in this question (Y*)? Show your work. Suppose also that for any $10 decrease in price, desired consumption will increase by $5. 2. Write down the equation for the Aggregate Demand Curve (AD) in the form of Y = a + bp. Show your work. 3. What is the current Short-Run Equilibrium value for Real GDP (Y) and the price level (p)? Show your work. 4. Draw the AD, AS, and LRAS curves. Label all x-intercepts and y-intercepts. Are we currently in an Inflationary Gap, Recessionary Gap, or in Long-Run Equilibrium? How do you know?
