Macro Inter chap 3: National Income: Where It Comes From and Where It Go

Problem 1 Suppose the production function in an economy is Y = K0.5L0.5, where K is the amount of capital and L is the term-1amount of labor. The economy begins with 81 units of capital and 9 units of labor. Round answers to two places after the decimal when necessary. a. How much output does the economy produce?

27 units of output

c. Now suppose that G rises to $3230. Compute the new private saving, public saving, and national saving. Private savings: $ Public savings: $ National savings: $

Public saving = -210

a. Suppose the government increases both taxes (T) and government purchases (G) by equal amounts. Assuming income (Y) is fixed by the factors of production, the change in national saving (ΔS) will be(MPC − 1) × ΔT.(1 − MPC) × ΔT. b. The larger is the MPC (the closer it is to 1), the will be the decline in investment, and the will be the increase in the interest rate.

(MPC − 1) × ΔT. The larger is the MPC (the closer it is to 1), the smaller will be the decline in investment, and the smaller will be the increase in the interest rate.

1. A manager of a perfectly competitive firm observes that the marginal product of labor is 5 units per hour, the marginal product of capital is 40 units per machine, the wage is $20 per hour, the rental price of capital is $120 per machine, and the price of output is $5 per unit. Please complete the following statement. To maximize profit, the manager should--- hire and--- .

In order to maximize profit, a perfectly competitive firm hires labor up to that point at which marginal revenue product of labor equals the wage rate. Marginal revenue product of labor = marginal product of labor * Price of output Marginal revenue product of labor = 5 * $5 = $25 Wage rate = $20 per hour Since, marginal revenue product of labor is greater than the wage rate, firm should hire more labor. In order to maximize profit, a perfectly competitive firm hire capital up to that point at which marginal revenue product of capital equals the wage rate. Marginal revenue product of capital = marginal product of capital * Price of output Marginal revenue product of capital = 40 * $5 = $200 Rental price of capital = $120 per hour Since, marginal revenue product of capital is greater than the rental price of capital, firm should hire more capital. Thus, To maximize profit, the manager should hire more labor and more capital.

Problem 2 Consider an economy with the given values. Y=C+I+G Y=$6400 G=$2970 T=$3020 C=$225+0.80(Y−T) I=$1000−50r Answer the following questions. a. Compute private saving, public saving, and national saving. Private savings: $ Public savings: $ National savings: $

Income = Output =Y Private saving = Income - Taxes - Consumption = 451 Public Saving = Taxes -Government Purchases = 50 National savings = Private Saving + Public Saving = 501

b. Given that the national savings rate you calculated in part a find the equilibrium interest rate. equilibrium interest rate: %

Investment = National Saving => r = 9.98%

d. If a sudden immigration quadruples the size of the population, while the capital stock is unchanged, what is the new level of output? new output: units e. What is the new wage and rental price of labor? new wage: unit(s) of output new rental price: unit(s) of output f. What is the new share of output labor receives? share out output to labor: %

K = 81, L= 9x4=36

An increase in the --- interest rate causes investment to ---

Real, decreases explain?

The Cobb-Douglas production function has the form Y = AKαL1 − α. That is, total output (Y) is a function of labor employed (L), capital employed (K), and the level of technology (A). Assume that α = 0.3. Use this information to answer the following questions. a. The marginal product of labor (MPL) can be expressed as ---, and the marginal product of capital (MPK) can be expressed as ---. In a competitive economy, firms pay a real wage (W/P) equal to the marginal product of labor (MPL) and a real rental rate (R/P) equal to the marginal product of capital (MPK). Note that labor's share of total income (Y) in the economy is represented by the product of the real wage and the total quantity of labor employed. Likewise, capital's share is represented by the product of the real rental rate and the total quantity of capital employed. Use this information to answer the following questions. b. Labor's share of total income (Y) in the economy can be expressed as ---, and capital's share of total income can be expressed as ---. c. This means that labor receives--- of total income, and capital receives--- of total income.

a. The marginal product of labor (MPL) can be expressed as (1−α)YL, and the marginal product of capital (MPK) can be expressed as αYK. b. Labor's share of total income (Y) in the economy can be expressed as (1 − α)Y, and capital's share of total income can be expressed as αY. c. This means that labor receives 70 percent of total income, and capital receives 30 percent of total income.

1. Use the neoclassical theory of distribution to predict the impact on the real wage and the real rental price of capital of each of the events described below. a. If an earthquake destroys some of the capital stock, then the real wage would --- and the real rental price of capital would ---. b. If a technological advance improves the production function, the real wage would ---, and the real rental price of capital would ---

a. decrease- increase b. increase- increase explain?

b. Calculate the wage and the rental price of capital. wage: unit(s) of output rental price: $ unit(s) of output c. What is the share of output labor receives? share of output to labor: %

b. New wage rate = marginal product of labour (MPL). Here MPL = 0.5K0.5L-0.5 = 0.5 * 9 * (1/16) = 0.28. Rental rate = marginal product of capital (MPK) = 0.5K-0.5L0.5 = 0.5*(1/9)*16 = 0.89. c. Labor Share = Wage x L/Y

A decrease in government purchases of goods and services, holding taxes constant, will--- the equilibrium real interest rate and--- investment.

explain?

Assume an economy has a national income of $1,200. Consumption is $600, taxes are $200, and government purchases are $300. Answer the following question. In this economy, national saving is$400.$300.$600.$500.

explain?

Suppose that an increase in consumer confidence raises consumers' expectations about their future income and thus increases the amount they want to consume today. This might be interpreted as an upward shift in the consumption function. a. In the graph below, (1) adjust the appropriate curve and (2) move the equilibrium point to reflect the impact of an increase in consumption today due to expectations of higher future income. Real Interest Rate (percent)Investment, Saving (trillions of dollars)012345678012345678Desired investment, I(r)National savingEquilibrium b. As a result of the change in consumer expectations, the interest rate falls, and investment rises.

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According to the neoclassical theory of distribution, a worker's real wage reflects her productivity. Let's use this insight to examine the incomes of two groups of workers: farmers and barbers. Let Wf and Wb be the nominal wages of farmers and barbers, Pf and Pb be the prices of food and haircuts, and MPLf and MPLb be the marginal productivity of farmers and barbers. a. Over the past century, the productivity of farmers (MPLf) has risen substantially because of technological progress. According to the neoclassical theory, what should have happened to farmers' real wage (Wf/Pf)? b. Over the past century, the productivity of barbers (MPLb) has remained constant. According to the neoclassical theory, what should have happened to farmers' real wage (Wb/Pb)? c. How are real wages measured in parts a and b?As output per worker times the price of the outputAs units of output per hour workedAs the ratio of capital to laborAs the ratio of output per worker to the price of the output d. Suppose workers can move freely between being farmers or being barbers (i.e., no additional costs are required to switch between occupations). What does this imply about the nominal wage of each occupation? e. Your answers in parts a through d imply that the relative price of haircuts, Pb, has relative to the price of food, Pf.

need more explain? a. Real wages should increase. b. Real wages should remain constant. c. As units of output per hour worked d. The nominal wages should be equal. e. risen

Assume an economy has the Cobb-Douglas production function Y = 10 K1/3 L2/3. If the economy's stock of capital doubles, the share of total income paid to the owners of capital will increase by 10 percent increase by one-third increase by two-thirds stay the same.

share of total income of Labor = exponent of L in Production function = 2/3, it will stay same share of total income paid to the owners of capital = exponent of K in Production function = 1/3, it will stay same

Consider a Cobb-Douglas production function with three inputs. K is capital (the number of machines), L is labor (the number of workers), and H is human capital (the number of college degrees among the workers). The production function is Y = K1/3L1/3H1/3. a. The expression for the marginal product of labor (MPL) can be found by taking the partial derivative of the Cobb-Douglas production function with respect to L: MPL = 1313(K1/3L−2/3H1/3). From this equation, how does an increase in the amount of human capital affect the marginal product of labor? An increase in human capital will the marginal product of labor. b. The expression for the marginal product of human capital (MPH) can be found by taking the partial derivative of the Cobb-Douglas production function with respect to H: MPH = 1313(K1/3L1/3H−2/3) From this equation, how does an increase in the amount of human capital (H) affect the marginal product of human capital? An increase in human capital will the marginal product of human capital. c. Total income paid to labor in the economy is the real wage times the quantity of labor. Under perfect competition, the real wage equals MPL, and the real earnings to human capital equal MPH. Total income in the economy, Y, is determined by the production function. What are the income shares paid to labor (L) and to human capital (H)? Labor's share of total income in the economy is . d. In the national incomes accounts, the share of national income going to workers in general would be e. An unskilled worker earns the marginal product of labor (MPL), whereas a skilled worker earns the marginal product of labor plus the marginal product of human capital (MPL + MPH). Consider the answers to questions a and b above. How would an increase in the amount of human capital in the economy (more college degrees) impact the share of income going to both skilled and unskilled workers? Decreasing returns means that increasing the number of college degrees in the economy will the wage premium enjoyed by workers holding a college degree. Increasing the number of college degrees will the earnings of unskilled workers in the economy.

An increase in human capital will raise the marginal product of labor. b. An increase in human capital will lower the marginal product of human capital. c. Labor's share of total income in the economy is 1/3. d. In the national incomes accounts, the share of national income going to workers in general would be 23 e. Decreasing returns means that increasing the number of college degrees in the economy will decrease the wage premium enjoyed by workers holding a college degree. Increasing the number of college degrees will increase the earnings of unskilled workers in the economy.

Assume immigration increases the labor force in an economy with a Cobb-Douglas production function. Please complete the following statement. As a result, the real wage ---, and the rental price of capital ---.

As per Cobb Douglas production function; Y = A(L^b)(K^a) where A: factor productivity L: Labor input K: capital input Now as immigration increases labor force thus real wages fall for the same amount of capital as surplus of labor will make labor wages lower. Rental price of capital will increase as capital will be scarse resource in this case as demand of capital rises as more labor demand more capital.

If a 10 percent increase in both capital and labor causes output to increase by less than 10 percent, the production function is said to exhibit decreasing returns to scale. If it causes output to increase by more than 10 percent, the production function is said to exhibit increasing returns to scale. Why might a production function exhibit decreasing or increasing returns to scale? Consider the three different scenarios (A, B, and C) described below. Place each scenario letter (A, B, or C) into the proper category, as most likely to exhibit either increasing or decreasing returns to scale in production. Scenario A: A small economy has many unemployed workers and much unused capital. However, the unemployed workers have less work experience and education than those currently working. An increase in demand for this nation's output causes all firms in the economy to hire 10% more workers and lease 10% more capital. Scenario B: A developing national economy currently employs a small percentage of its available labor force and capital. Increased global demand for the output of this nation's economy requires its firms to employ 10% more labor and 10% more capital. This change allows firms to try new and novel combinations of labor and capital in their production processes. Scenario C: A small island nation's economy consists solely of commercial fishing firms. These firms currently employ modest boats manned by small crews to efficiently harvest all of the 10 mile off-shore perimeter of the nation's sovereign ocean waters. Each day, these boats go out to sea and return to the island to deliver their catch to buyers. A new treaty expands this legal fishing area to a 20 mile off-shore perimeter. The firms respond by employing 10% more boats and 10% more crews to exploit this new opportunity. Increasing Returns to Scale: Decreasing Returns to Scale:

If increasing all inputs by N%, output increases by more than (less than) N%, there are increasing (decreasing) returns to scale. Therefore: Increasing returns to scale: - Scenario B [Reason: New production methods may increase efficiency of both inputs] Decreasing returns to scale: - Scenario A [Reason: Unemployed workers have less experience, so will not be as productive as those already working] - Scenario C [Reason: Doubling the fishing perimeter does not enable catching of more than double the amount of fish]