We can combine the models we have seen so far to explain both real GDP and the price level in the long run. Real GDP is determined according to the production model, which is summarized in Table 4.1 of your textbook where the aggregate production function is Cobb-Douglas with labor share equal to 2/3. The price level is obtained from the quantity theory, which is summarized in Table 8.3 of your textbook. The nominal wage (in dollars) is the product of the real wage and the price level.(i) Express the equilibrium real wage as a function of the capital stock, labor force, and TFP. Express the equilibrium nominal wage as a function of the money supply, velocity of money, and labor force.(ii) Suppose TFP increases. What happens to the real and nominal wages?(iii) Suppose the money supply increases. What happens to the real and nominal wages?Your answers must be detailed and you must provide the different steps leading to your conclusions. **Table 4.1: The Production Model: 5 Equations and 5 Unknowns**This table outlines a production model using five equations with five unknowns. Here's a detailed transcription and explanation:**Unknowns/endogenous variables:**- $ Y $ (Output)- $ K $ (Capital used)- $ L $ (Labor used)- $ r $ (Rental rate of capital)- $ w $ (Wage rate)**Production function:**\[ Y = A \overline{K}^{1/3} L^{2/3} \]This equation models the output $ Y $ as a function of capital $ K $ and labor $ L $, with productivity parameter $ A $. The exponents $ \frac{1}{3} $ for capital and $ \frac{2}{3} $ for labor represent their respective contributions to production.**Rule for hiring capital:**\[ \frac{1}{3} \cdot \frac{Y}{K} = r \]This equation determines the condition for hiring capital. It suggests that the marginal product of capital should equal the rental rate ($ r $).**Rule for hiring labor:**\[ \frac{2}{3} \cdot \frac{Y}{L} = w \]This condition is used for hiring labor, requiring the marginal product of labor to equal the wage rate ($ w $).**Demand = Supply for capital:**\[ K = \overline{K} \]This implies that the demand for capital equals the supply of capital.**Demand = Supply for labor:**\[ L = \overline{L} \]This indicates that the demand for labor is equal to the supply of labor.**Parameters/exogenous variables:**- $ A $ (Total factor productivity)- $ \overline{K} $ (Fixed supply of capital)- $ \overline{L} $ (Fixed supply of labor)This model is foundational in understanding how different factors contribute to production and how market conditions influence factor usage and compensation.

Optimal level of employment for any input is achieved at the point where the value of marginal product of the input is equal to the input price . Given , Labor input price = w Capital input price = r a .) Equilibrium level of labor employment would be achieved at the point where , VMP(L)= w VMP(L) = Output price *Marginal product of labor MP(L) = d(Y)/dL = AK1/3/L1/3 Let the output price be (p ) - VMP(L)= p*AK1/3/L1/3 Putting values in the optimal condition - p*AK1/3/L1/3 = w Let real wage : w/p = Wr L* = (A/ Wr)3 K (Labor demand as a function of A ,real wage and capital) Wr* = AK1/3/L1/3 (Real wage as a function of labor force , A and Capital ) ---(i ) According to Fischer's equation - M*V = P*Y Where , M = Money supply , V = velocity of money , P = Price level , Y = Output Putting the value of P from above equation into the optimal labor demand equation - w = (MV)AK1/3/YL1/3 ----(ii ) b. ) From equation (i ) : Wr* = AK1/3/L1/3 Rate of change of Wr w.r.t TFP : d(Wr)/dA d(Wr)/dA => K1/3/L1/3 ( which is positive because neither of the labor or capital can be negative ) d(Wr)/dA > 0 So the real wage and TFP are directly proportional . And , Similarly d(w)/dA = p K1/3/L1/3 (Which is also positive ) Therefore , both the real and nominal wages are directly proportional . c .) To find the impact of change in money supply of nominal wage we use equation (ii) - d(w)/dM = V)AK1/3/YL1/3 ( Which is positive as V, A, L , Y & K all the positive ) d(w)/dM > 0 So , as the money supply increases nominal wage increases . But , as real wage = w/ P There would be an increase in both (w) and P(according to fisher's equation ) . So the change in real wage would be dependent on the extent of change in both (w) & P . If , ∆w > ∆p ( Real wage would increase ) If , ∆w < ∆p (Real wage would decline )

Business

Economics

We can combine the models we have seen so far to explain both real GDP and the price level in the long run. Real GDP is determined according to the production model, which is summarized in Table 4.1 of your textbook where the aggregate production function is Cobb-Douglas with labor share equal to 2/3. The price level is obtained from the quantity theory, which is summarized in Table 8.3 of your textbook. The nominal wage (in dollars) is the product of the real wage and the price level. (i) Express the equilibrium real wage as a function of the capital stock, labor force, and TFP Express the equilibrium nominal wage as a function of the money supply, velocity of money, and labor force. (ii) Suppose TFP increases. What happens to the real and nominal wages? (iii) Suppose the money supply increases. What happens to the real and nominal wages? Your answers must be detailed and you must provide the different steps leading to your

We can combine the models we have seen so far to explain both real GDP and the price level in the long run. Real GDP is determined according to the production model, which is summarized in Table 4.1 of your textbook where the aggregate production function is Cobb-Douglas with labor share equal to 2/3. The price level is obtained from the quantity theory, which is summarized in Table 8.3 of your textbook. The nominal wage (in dollars) is the product of the real wage and the price level. (i) Express the equilibrium real wage as a function of the capital stock, labor force, and TFP Express the equilibrium nominal wage as a function of the money supply, velocity of money, and labor force. (ii) Suppose TFP increases. What happens to the real and nominal wages? (iii) Suppose the money supply increases. What happens to the real and nominal wages? Your answers must be detailed and you must provide the different steps leading to your

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

From 2009 to 2019, suppose that GDP increased by 25 percent. Real GDP increased by 15%. The overall level of prices increased by about 10% 20% 15% 5%
The table below shows the total expenditure on a basket of goods and services. Use this information to calculate index numbers for the cost of a basket of goods and services in each period. Assume Period 1 is the base year. Round to one decimal place. Provide your answer below: Period 1 Period 2 Period 3 Period 4 Total Expenditure $1,100 $1,350 $1,400 $1,450 Period 1 Period 2-Period 3 = Period 4 = | Index Number
During this pandemic-recession, it is likely that many people (particularly females with children) who are officially counted as not in labor force actually should be counted as a) unemployed b) employed
Consider the exhibit below for the following questions. Figure 33-4 Refer to Figure 33-4. If the economy starts at A and moves to D in the short run, the economy moves to A in the long run. moves to B in the long run. moves to C in the long run. stays at D in the long run.
Price level (GDP deflator, 2012=100) What happens in the economy when firms are no longer able to meet the demand for their output? Draw an aggregate demand curve. Label it AD. 135- Draw an aggregate supply curve. Label it AS. 125- Draw a point at the short-run macroeconomic equilibrium. Label it 1. Draw a point on the AS curve at which firms are unable to meet the demand for their output. Label it 2. 115- Prices When firms are unable to meet the demand for their output, 105- A. short-run aggregate supply is greater than long-run aggregate supply; rise 95- O B. the quantity of real GDP demanded is greater than the quantity of real GDP supplied; rise C. aggregate demand is greater than short-run aggregate supply; 85+ 18.0 19.0 20.0 21.0 22.0 rise Real GDP (trillions of 2012 dollars) D. the quantity of real GDP supplied is greater than the quantity of real GDP demanded; >>> Draw only the objects specified in the question. fall Click the graph, choose a tool in the palette and follow the…
What is the definition of labor productivity? Please list the factors that affect labor productivity. President Bush lowered income taxes for individuals in 2001. Explain how lower income taxes affect the aggregate demand curve.
Refer to the figure below. Which of the points in the above graph are possible short-run equilibria? Price level (GDP deflator, 2000 = 100) O A and B O A and C O A and D O A, B, C, and D LRAS SRAS, SRAS₂ AD₂ AD₁ Real GDP (trillions of 2000 dollars)